Mathematics Colloquium

מארגן/מארגנים: 
Usual Time: 
Place: 

Upcoming Lectures

Elon Lindenstrauss
30/04/2017 - 14:00 - 15:00
Arithmetic quotients of algebraic groups such as the space of unit volume lattices in R^n can be studied fruitfully from many directions and contain deep and subtle arithmetic information. Homogeneous dynamics studies these spaces by considering the action of a subgroup of the algebraic group on such a quotient. Of particular interest is the action of multiparameter diagonal groups: these display remarkable rigidity properties that are absent in the context of one parameter diagonalizable group actions.
 
One aspect of this rigidity is joining rigidity: under suitable conditions, this rigidity implies that knowing that an orbit of a multiparameter diagonalizable group in a product of two arithmetic quotients is equidistributed in each one of these quotients individually implies joint equidistribution.
 
I would explain this phenomena as well as some arithmetic consequences.

Previous Lectures

Gal Binyamini
23/04/2017 - 14:00 - 15:00
The problem of bounding the number of rational or algebraic points of a given height in a transcendental set has a long history. In 2006 Pila and Wilkie made fundamental progress in this area by establishing a sub-polynomial asymptotic estimate for a very wide class of transcendental sets. This result plays a key role in Pila-Zannier's proof of the Manin-Mumford conjecture, Pila's proof of the Andre-Oort conjecture for modular curves, Masser-Zannier's work on torsion anomalous points in elliptic families, and many more recent developments.
I will briefly sketch the Pila-Wilkie theorem and the way it enters into the arithmetic applications. I will then discuss recent work on an effective form of the Pila-Wilkie theorem (for certain sets) which leads to effective versions of many of the applications. I will also discuss a joint work with Dmitry Novikov on sharpening the asymptotic from sub-polynomial to poly-logarithmic for certain structures, leading to a proof of the restricted Wilkie conjecture. The structure of the systems of differential equations satisfied by various transcendental functions plays a key role for both of these directions.
Prof. Omri Sarig, Weizmann Institute of Science
02/04/2017 - 14:00 - 15:30

 "Symbolic dynamics" is a powerful technique for describing the combinatorial structure of large collections of orbits of dynamical systems with "chaotic" behaviour. I will describe this technique, and will report on recent advances on the question what sort of "chaos" is needed to this method to succeed. The talk is meant for a general audience, including people with little or no background in dynamical systems.

 

Prof. Ron Adin  
26/03/2017 - 14:00 - 15:30

Descents of permutations have been studied for more than a century. This concept was vastly generalized, in particular to standard Young tableaux (SYT). More recently, cyclic descents of permutations were introduced by Cellini and further studied by Dilks, Petersen and Stembridge. Looking for a corresponding concept for SYT, Rhoades found a very elegant solution for rectangular shapes. In an attempt to extend the concept of cyclic descents, explicit combinatorial definitions for two-row and certain other shapes have been found, implying the Schur-positivity of various quasi-symmetric functions. In all cases, the cyclic descent set admits a cyclic group action and restricts to the usual descent set when the letter n is ignored. Consequently,

the existence of a cyclic descent set with these properties was conjectured for all shapes, even the skew ones. This talk will report on the surprising resolution of this conjecture: Cyclic descent sets exist for nearly all skew shapes, with an interesting small set of exceptions. The proof applies non-negativity properties of Postnikov's toric Schur polynomials and a new combinatorial interpretation of certain Gromov-Witten invariants. We shall also comment on issues of uniqueness. Based on joint works with Sergi Elizalde, Vic Reiner, Yuval Roichman.

            

Dr. Menachem Shlossberg invites you to a “haramat kosit” in celebration of obtaining a postdoctorate

at the University of Udine, Italy, at 1:30 PM next to the Colloquium Room

ד"ר מנחם שלוסברג מזמין אתכם להרמת כוסית לרגל קבלת משרת פוסט דוקטורט באונ' אודין באיטליה

 בשעה 13:30 בחדר ע"י חדר המחלקה

 

 

Iosif Polterovich, University of Montreal
19/03/2017 - 14:00 - 15:30

The sloshing problem is a Steklov type eigenvalue problem describing small oscillations of an ideal fluid. We will give an overview of some latest advances in the study of Steklov and sloshing spectral asymptotics, highlighting the effects arising from corners, which appear naturally in the context of sloshing. In particular, we will outline an approach towards proving the conjectures posed by Fox and Kuttler back in 1983 on the asymptotics of sloshing frequencies in two dimensions. The talk is based on a joint work in progress with M. Levitin, L. Parnovski and D. Sher.

 

Ilan Barnea
05/02/2017 - 14:00 - 15:00

Model categories, introduced by Quillen, provide a very general context in which it is possible to set up the basic machinery of homotopy theory. In particalar they enable to define derived functors, homotopy limits and colimits, cohomology theories and spectral sequences to catculate them. However, the structure of a model category is usually hard to verify, and in some interesating cases even impossible to define. In this lecture I will define a much simpler notion then a model category, called a weak fibration category. By a theorem due to T. Schlank and myself, a weak fibration category gives rise in a natural way to a model category structure on its pro category, provided some technical assumptions are satisfied. This result can be used to construct new model structures in different mathematical fields, and thus to import the methods of homotopy theory to these situations. Examples will be given from the categories of simplicial presheaves, C*-algebras and complexes in Abelian categories. Applications will be discussed with each example.

The above encompasses joint work with Tomer M. Schlank, Yonatan Harpaz, Geoffroy Horel, Michael Joachim Snigdhayan Mahanta and Matan Prezma.

 

Alexander Fish, School of Mathematics and Statistics, University of Sydney, Australia
22/01/2017 - 14:00 - 15:00

 

We present a new approach (joint with M. Bjorklund (Chalmers))  for finding new patterns in difference sets E-E, where E has a positive density in Z^d, through measure rigidity of associated action.  

By use of measure rigidity results of Bourgain-Furman-Lindenstrauss-Mozes and Benoist-Quint for algebraic actions on homogeneous spaces, we prove that for every set E of positive density inside traceless square matrices with integer values, there exists positive k such that the set of characteristic polynomials of matrices in E - E contains ALL characteristic polynomials of traceless matrices divisible by k.

By use of this approach Bjorklund and Bulinski (Sydney), recently showed that for any quadratic form Q in d variables (d >=3) of a mixed signature, and any set E in Z^d of positive density the set Q(E-E) contains kZ for some positive k. Another corollary of our approach is the following result due to Bjorklund-Bulinski-Fish: the discriminants D = {xy-z^2 , x,y,z in B} over a Bohr-zero non-periodic set B covers all the integers.

Boris Khesin, University of Toronto
01/01/2017 - 14:00 - 15:00

A plane curve is called nondegenerate if it has no inflection points.

How many classes of closed nondegenerate curves exist on a sphere?

We are going to see how this geometric problem, solved in 1970, reappeared along with its generalizations  in the context of the Korteweg-de Vries and Boussinesq equations. Its discrete version is related to the 2D pentagram map defined by R. Schwartz in 1992.

We will also describe its generalizations, pentagram maps on polygons in any dimension and discuss their integrability properties.

 

 

Adam Sheffer
18/12/2016 - 14:00 - 15:00

While the topic of geometric incidences has existed for several decades, in recent years it has been experiencing a renaissance due to the introduction of new polynomial methods. This progress involves a variety of new results and techniques, and also interactions with fields such as algebraic geometry and harmonic analysis.

A simple example of an incidences problem: Given a set of n points and set of n lines, both in R^2, what is the maximum number of point-line pairs such that the point is on the line. Studying incidence problems often involves the uncovering of hidden structure and symmetries.

In this talk we introduce and survey the topic of geometric incidences, focusing on the recent polynomial techniques and results (some by the speaker). We will see how various algebraic and analysis tools can be used to solve such combinatorial problems.

 

Edva Roditty-Gershon, Bristol University
11/12/2016 - 14:00 - 15:00

In the talk I will discuss classical problems concerning the distribution of square-full numbers and their analogues over function fields. The results described are  in the context of the ring Fq[T ] of polynomials over a finite field Fq of q elements, in the limit q → ∞. 

I will also present some recent generalization of these kind of classical problems.

Assaf Rinot
27/11/2016 - 14:00 - 15:00
In the early 1970's, Hindman proved a beautiful theorem in additive Ramsey theory asserting that for any partition of the set of natural numbers into finitely many cells, there exists some infinite set such that all of its finite sums belong to a single cell.
 
In this talk, we shall study generalizations of this statement. Among other things, we shall present a negative partition relation for the real line which simultaneously generalizes a recent theorem of Hindman, Leader and Strauss, and a classic theorem of Galvin and Shelah.
 
This is joint work with D.J. Fernandez Breton from the University of Michigan.
Prof. Arkady Berenstein, University of Oregon
20/11/2016 - 14:00 - 15:00

Hecke algebras H_q(W) of Coxeter groups W first emerged in the study of Chevalley groups in mid sixties and since then became central objects in Representation Theory of Coxteter groups and semisimple Lie groups over finite fields. In particular, as a one-parameter deformation of the group algebra kW of W, the Hecke algebra H_q(W) helps to classify representations of W and to equip each simple kW-module with the canonical Kazhdan-Lusztig basis.
Unfortunately, unlike the group algebra kW, the Hecke algebra H_q(W) lacks a Hopf algebra structure, that is, it is not clear how to tensor multiply H_q(W)-modules. Moreover, there is a general consensus that a naive Hopf structure on H_q(W), if exists, would essentially coincide with that on kW, so we would not gain any new information.
In my talk (based on joint work with D. Kazhdan) I suggest a roundabout: instead of forcing a naive Hopf structure on H_q(W), we find a ``reasonably small" Hopf algebra H(W) (we call it Hecke-Hopf algebra of W) that "naturally" contains H_q(W) as a coideal subalgebra.
The immediate benefit of this enlargement of H_q(W) is that each representation of H(W) and each representation of H_q(W) can be tensor multiplied into a new representation of H_q(W), thus allowing to create infinitely many new H_q(W)-modules out of a single one.
Hecke-Hopf algebras have some other applications, most spectacular of which is the construction of new infinite families of solutions to the quantum Yang-Baxter equation.

Piotr Szewczak
13/11/2016 - 14:00 - 18:20

The theory of selection principles deals with the possibility of obtaining mathematically significant objects by selecting elements from sequences of sets. The studied properties mainly include covering properties, measure- and category-theoretic properties, and local properties in topological spaces, especially functions spaces. Often, the characterization of a mathematical property using selectionprinciple is a nontrivial task leading to new insights on the characterized property.

I will give an overview of this theory and, if time permits, present some resent results obtained jointly with Boaz Tsaban and Lyubomyr Zdomskyy.

Nir Lev, Dept. of Mathematics, Bar-Ilan University
06/11/2016 - 14:00 - 15:30

We know by classical Fourier analysis that the unit cube in R^d has an orthogonal basis consisting of exponential functions. Which other domains admit such a basis? Fuglede conjectured (1974) that these so-called "spectral domains" could be characterized geometrically by their possibility to tile the space by translations. I will survey the subject and then discuss some recent results, joint with Rachel Greenfeld, where we focus on the conjecture for convex polytopes.

 

Ari Meir Brodsky
19/06/2016 - 12:00 - 13:00

We explore results of Ramsey theory (also known as partition calculus) and show how they apply to cardinals, ordinals, trees, and arbitrary partial orders, leading up to the main result which is a generalization to trees of the Balanced Baumgartner-Hajnal-Todorcevic Theorem.

 

A full exposition of the results is contained in my PhD thesis, available at http://hdl.handle.net/1807/68124.

Dr. Victoria Sevostyanova (Haifa U.)
29/05/2016 - 12:00 - 13:00

Hilbert’s fourteenth problem asks whether the algebra of invariants for an action of a linear algebraic group is finitely generated.
This is true for reductive groups and the problem is open for unipotent groups. We discuss the case of the adjoint action of a maximal unipotent subgroup U in GL_n(K) on the nilradical m of any parabolic subalgebra, where K is an algebraically closed field of zero characteristic. This action is extended to a representation in the algebra K[m]. I will show that the algebra of invariants K[m]^U is finitely generated. Besides, a set of algebraically independent invariants generating the field K(m)^U
 will be presented.

Erick Herbin, Ecole Centrale Paris
22/05/2016 - 12:00 - 13:00

We consider the issue of generalized stochastic processes, indexed by an abstract set of indices. What should the minimal required conditions on the indexing collection be, to study some of the usual properties of these processes, such as in- crement stationarity, martingale and Markov properties or integration question? The already known examples of processes indexed by functions or metric spaces can be addressed by this way. 

We show how the set-indexed framework of Ivanoff-Merzbach allows to study these generalized processes.

Some set-indexed processes can be considered as random measures on some δ- ring. Some generalized processes can be defined as an integral with respect to some measure on the indexing collection. The example of set-indexed Lévy processes is considered. The links with function-indexed processes could be discussed.

If time permits, we could also discuss regularity issue : continuity or Hölder regularity.

This talk is based on works in collaboration with Ely Merzbach and Alexandre Richard. 

Assaf Rinot
15/05/2016 - 12:00

Recall that the real line is that unique separable, dense linear ordering with no endpoints in which every bounded set has a least upper bound.
Around the year of 1920, Souslin asked whether the term *separable* in the above characterization may be weakened to *ccc*. (A linear order is said to be separable if it has a countable dense subset. It is ccc if every pairwise-disjoint family of open intervals is countable.)
Amazingly enough, the resolution of this single problem led to many key discoveries in set theory. Also, consistent counterexamples to this problem play a prominent role in infinite combinatorics.

In this talk, we shall tell the story of the Souslin problem, and report on an advance recently obtained after 40 years of waiting.

 

Yoav Segev (BGU)
08/05/2016 - 12:00 - 13:00

Jordan algebras J of charateristic not 2 sometimes contain
a set of idempotents (e^2=e) that generate J such that  their adjoint
map ad_e: u \mapsto ue (u\in J) has the minimal polynomial
x(x-1)(x-1/2), and with additional restrictions on products
of elements in the eigenspaces of ad_e (for each e).

Generalizing these properties (not only of such Jordan
algebras) Hall, Rehren, Shpectorov (HRS) introduced ``Axial algebras
of Jordan type''.  In my talk I will present structural results
on Axial algebras of Jordan type 1/2 (a case which was not
dealt with in HRS), I will discuss their idempotents e,  the corresponding
``Miyamoto involutions'' \tau(e) and the group that these involutions 
generate.

This is joint work with J. Hall, S. Shpectorov.

Boris Zilber (Oxford)
27/03/2016 - 12:00 - 13:00
In 1988 Hrushovski found counterexamples to the speaker's conjectures that categorical theories are in a certain sense reducible to algebraic geometry.  Actually, the counterexamples are the outcomes of a very special abstract construction which is based on a combinatorial inequality in terms of dimensions of algebraic origin. The counterexamples were originally perceived as unwelcome mathematical pathologies.
We will explain how Hrushovski's construction can be linked to
the theory of classical transcendental functions  and how it leads to certain conjectures  which eventually can be recognised as a form of Grothendieck - Andre period conjecture.
Prof. Jerzy Kąkol
20/03/2016 - 12:00 - 13:00

Corson (1961) started a systematic study of certaintopological properties of the weak topology w of Banach spaces E. This
line of research provided more general classes such as reflexive
Banach spaces, Weakly Compactly Generated Banach spaces and the class
of weakly K-analytic and weakly K-countably determined Banach spaces.
On the other hand, various topological properties generalizing
metrizability have been studied intensively by topologists and
analysts. Let us mention, for example, the first countability,
Frechet-Urysohn  property, sequentiality, k-space property, and
countable tightness. Each property (apart the countable tightness)
forces a Banach space E to be finite-dimensional, whenever E with the
weak topology w  is assumed to be a space of the above type. This is a
simple consequence of a theorem of Schluchtermann and Wheeler that an
infinite-dimensional Banach space is never a k-space in the weak
topology. These results show also that the question when a Banach
space endowed with the weak topology is homeomorphic to a certain
fixed model space from the infinite-dimensional topology is very
restrictive and motivated specialists to detect the above  properties
only for some natural classes of subsets of E, e.g., balls or bounded
subsets of E. We collect some classical and recent results of this
type, and characterize those Banach spaces E whose unit ball B_w is
k_R-space or even has the Ascoli property. Some basic concepts from
probability theory and measure theoretic properties of the space l_1
will be used.

Dr. M. Schein, (Bar Ilan)
13/03/2016 - 12:00 - 13:00

A finitely generated group $G$ has only a finite number, say $a_n(G)$, of subgroups of any given index $n$.  The study of subgroup growth, i.e. of the behavior of this sequence, has been an active area of research for several decades.  A variant problem investigates the sequence $a_n^\wedge (G)$ counting subgroups of index $n$ whose profinite completion is isomorphic to that of the original group $G$, and in particular the analytic properties of the Dirichlet series derived from this sequence.

 

 
The computation of these Dirichlet series turns out to be equivalent to the computation of some p-adic integrals over algebraic groups; integrals of this type have been studied extensively since the 1960's.  Each of these two ways of approaching what turns out to be the same problem sheds light on the other.
 
The talk will discuss the connection between pro-isomorphic subgroups and p-adic integrals.  It will also discuss recent joint work with Mark Berman on the behavior of pro-isomorphic zeta functions under base extension.  No knowledge of the subject will be assumed.
Prof. Eli Shamir, Hebrew University, Jerusalem
06/03/2016 - 12:00 - 13:00
The key concept of our discussion is that of a perfect matching (PM) in a bipartite graph.
The expansion condition in Hall's marriage theorem can be extended to an unbiased 2-sided one.
This enables an alternative (and simpler) proof of Evans' (proven) Conjecture:
A partial nxn Latin square with n-1 dictated entries admits a completion to a full Latin square. 
PMs are used to successively fill the square by rows, columns or diagonals. Latin square tables correspond to quasi-groups; the ones corresponding to groups are only a tiny fraction of them, as n grows. However, for Sudoku tables of order mnxmn, the completion (say by diagonals) usually fails, even if there are no dictated entries, unless they are conjugates of a twisted product of two groups, of orders n and m.
 
Leonid Makar -Limanov
03/01/2016 - 12:00 - 13:00
Yitang Zhang who became famous recently thanks to brake-through in the twins conjecture wrote his PhD thesis on the plane Jacobian conjecture where he gave an estimate of the geometric degree of the corresponding mapping of a plane via algebraic degrees of the images of the coordinate functions. In  my talk I'll explain how to gets a better estimate via the Newton polytope approach.
 
Mira Shamis
27/12/2015 - 12:00 - 13:00

We shall discuss the Chirikov standard map, an area-preserving map of the torus to itself in which quasi-periodic and chaotic dynamics are believed to coexist. We shall describe how the problem can be related to the spectral properties of a one-dimensional discrete Schroedinger operator, and present a recent result.

Based on joint work with T. Spencer.

Eugenii Shustin
20/12/2015 - 12:00 - 13:00

We define refined tropical enumerative invariants counting plane tropical curves of a given degree and a given positive genus and having marked points on edges and at vertices. This extends Block-Goettsche and Goettsche-Schroeter refined tropical invariants. As a consequence we obtain tropical (complex) descendant invariants and (real) broccoli invariants of positive genus.

(Joint work with F. Schroeter.)

 
William I. Newman (UCLA)
06/12/2015 - 12:00 - 13:00

We consider both time series as well as spatial distributions (in 1-4 dimensions). In the first, we observe that time series for individual and independently deviating random variables can manifest pattern  through the emergence of peak-to-peak sequences that are visible to the eye yet fail all Fourier analysis schemes and reveal a seeming periodicity of 3-events per cycle.  We note that this can explain observations of apparent cycles in mammalian animal populations.  We consider models, as well, based on the Langevin equation of kinetic theory and the Smolouchowski relation that present circumstances where the apparent period can vary from 3-4 and, for a special subclass of problems, to periods between 2 and 3. We explore how cataloged observational data from global earthquake catalogues, magnetospheric AL index observations, Old Faithful Geyser eruption data, and the performance of the Standard & Poor's 500 index (percent daily variation) manifest different degrees of statistical agreement with the theory we derived.  We present a simple model for many mammalian population cycles whose underlying phenomenological basis has strong biological implications.     We then employ directed graphs to explore nearest-neighbor relationships and isolate the character of spatial clustering in 1-4 dimension.  We observe that the one-dimensional problem is formally equivalent to that presented by peak-to-peak sequences in time series and also demonstrates a mean number of points per cluster   of 3 in one dimension. We then take the first moment of each of the clusters formed, and observed that they too form clusters. We observe the emergence of a hierarchy of clusters and the emergence of universal cluster numbers, analogous to branching ratios and, possibly, Feigenbaum numbers.  These, in turn, are related to fractals as well as succularity and lacunarity, although the exact nature of this connection has not been identified.  Finally, we show how hierarchical clustering emerging from random distributions may help provide an explanation for observations of hierarchical clustering in cosmology via the virial theorem and simulation results relating to the gravitational stabilization in a self-similar way of very large self-gravitating ensembles. 

Ido Efrat (BGU)
29/11/2015 - 12:00 - 13:00

These symmetry patterns are described by the absolute Galois group of the field, whose
structure is in general still a mystery.

We will describe what is known about this symmetry group: classical facts, consequences 
of the epochal work by Veovodsky and Rost, and very recent structural results and conjectures
related to higher cohomology operations and intersection theorems.

Yaar Solomon (Stony Brook University)
22/11/2015 - 12:00 - 13:00

Is there a point set Y in R^d, and C>0, such that every convex set of volume 1 contains at least one point of Y and at most C?   This discrete geometry problem was posed by Gowers in 2000, and it is a special case of an open problem posed by Danzer in 1965. I will present two proofs that answers Gowers' question with a NO. The first approach is dynamical; we introduce a dynamical system and classify its minimal subsystems. This classification in particular yields the negative answer to Gowers' question. The second proof is direct and it has nice applications in combinatorics. The talk will be accessible to a general audience. [This is a joint work with Omri Solan and Barak Weiss]. 

 
Eli Matzri
15/11/2015 - 12:00 - 13:00
The Merkurjev-Suslin Theorem tell us that the n-torsion part of the Brauer group of a field containing a primitive n-th root of 1 is generated by symbol algebras. A natural question is:What can be said on the minimal number of symbols needed.
In this talk I will survey some of the known results and give the idea for the proof for a bound in a geometric situation (by which I mean when the base field contains an algebraically closed field). 
 
Boris Kunyavskii (Bar-Ilan University)
08/11/2015 - 12:00 - 13:00

In 1846, Arthur Cayley defined a correspondence between orthogonal
matrices of determinant one and skew-symmetric matrices. This
observation was a starting point of a long (and yet unfinished)
story. In the talk we will overview its highlights, with a focus on
the achievements obtained during the past decade and some open
problems.

 
Prof. Boris Levit, Queen's University, Kingston, Canada
31/05/2015 - 12:00 - 13:00
The classical Abel-Jacobi elliptic functions have been extensively
used in the Approximation Theory and, in particular, in the Optimal Recovery problems. Such functions posses a variety of very attractive properties, being much more  exible and versatile in comparison to the circular functions. I will consider several examples of linear interpolating spaces generated by such functions. A notion of an optimal interpolating space will be discussed, drawing on some applications in statistical problems of random data approximation. Conditions will be presented under which the interpolating spaces generated by the Abel-Jacobi elliptic functions contain constants and are optimal, in the case of equidistant interpolating design. I will also mention some open problems related to a possible extension of these results to the more general class of automorphic functions.
Prof. Boris Levit, Queen's University, Kingston, Canada
31/05/2015 - 12:00 - 13:00
The classical Abel-Jacobi elliptic functions have been extensively
used in the Approximation Theory and, in particular, in the Optimal Recovery problems. Such functions posses a variety of very attractive properties, being much more  exible and versatile in comparison to the circular functions. I will consider several examples of linear interpolating spaces generated by such functions. A notion of an optimal interpolating space will be discussed, drawing on some applications in statistical problems of random data approximation. Conditions will be presented under which the interpolating spaces generated by the Abel-Jacobi elliptic functions contain constants and are optimal, in the case of equidistant interpolating design. I will also mention some open problems related to a possible extension of these results to the more general class of automorphic functions.
Alexander I. Bufetov (CNRS, Steklov, IITP, NRU-HSE)
10/05/2015 - 12:00 - 13:00

Let mu_{m,n} be the canonical invariant measure on the Grassmann manifold
of m-dimensional subspaces in C^{m+n}; the flat coordinates on the Grassmann
manifold allow us to consider mu_{m,n} as a measure on the space Mat(m x n) of
complex matrices. By definition, the family of measures mu_{m,n}  has
the property of consistency under natural projections
Mat((m + 1)  n) ---> Mat(m  n) ; Mat(m x (n + 1)) ---> Mat(m x n)
and consequently defines a probability measure  on the space Mat of infinite
complex matrices. The measure mu is by definition unitarily-invariant and admits
a natural one-parameter family of unitarily-invariant deformations mu^(s), called
the Pickrell measures. The Pickrell measures are finite for s > -1 and infinite
for s < 0.

The first main result of the talk is the solution to the problem, posed by
Borodin and Olshanski in 2000, of the explicit description of the ergodic decomposition of infinite Pickrell measures. The decomposing measures are naturally identified with sigma-finite processes on the half-line R+ and can be viewed as sigma-finite analogues of determinantal point processes. For different values of the parameter s, these measures are mutually singular.


In the second part of the talk we will discuss absolute continuity and singularity of determinantal point processes. The main result here is that determinantal point processes on Z induced by integrable kernels are indeed quasi-invariant under the action of the in nite symmetric group. The Radon-Nikodym derivative is found explicitly. A key example is the discrete sine-process of Borodin, Okounkov and Olshanski. This result has a continuous counterpart: namely, that
determinantal point processes with integrable kernels on R, a class that includes processes arising in random matrix theory such as the sine-process, the process with the Bessel kernel or the Airy kernel, are quasi-invariant under the action of the group of di eomorphisms with compact support.

The first part of the talk is based on the preprint http://arxiv.org/abs/1312.3161;
the second part, on the preprint http://arxiv.org/abs/1409.2068.

Leonid Polterovich (Tel-Aviv University)
03/05/2015 - 12:00 - 13:00

In 1990 Helmut Hofer introduced a bi-invariant metric on symplectomorphism
groups which nowadays plays an important role in symplectic topology and Hamiltonian dynamics.
I will review some old, new and yet unproved results in this direction.

Martin Markl (Academy of Sciences of the Czech Republic)
26/04/2015 - 12:00 - 13:00

Although higher structures have been around for quite some time, they recently have come back into focus through renewed interest in higher categories. There are several reasons for this.

In geometry one is trying to interpret extended cobordism theories, where the higher structures are meant to mimic higher codimensions. An analogue in algebra is known to the 2-categorical level, the prime example being the 2-category of rings, bi-modules and bi-module morphisms. Beyond this there are many open questions of fundamental nature. The central problem is what type of coherence to require.

In physics higher structures naturally appear in two related fashions. The first is through the extended field theories and the second through field theories with defects. This is mathematically mimicked by cobordisms and defect lines and points abstractly interpreted as inclusions into higher dimensional objects.

The "truncated" versions of higher structures can be assembled into infinity up to a homotopy everything version. This is the setting of the influential program of Lurie which provides firm foundations to derived algebraic geometry, and, hopefully, to higher differential geometry which is not yet that well established.

Geometric and physical points of view combine in the constructions of string topology and in the proofs of the cobordism hypothesis. One approach to this, which will also be an integral part of this program, is the operadic/monadic point of view as many liigher categorical structures can be interpreted as actions of certain liigher dimensional operads/monads. The classical homotopy theory teaches us that this is the correct way to encode higher homotopies and homotopical algebra in general.

The complexity of higher dimensional structures and necessity to work with them efficiently has required reconsideration of the foundations of mathematics. A new theory called univalent foundations or homotopy type theory emerges in recent years which has a potential to become a common language for mathematicians working with higher categorical structures. We wish to include this theory as a supplement to our main topics, but also as a possible future direction of research.

 

Andrzej Kisielewicz (Wroclaw)
19/04/2015 - 12:00 - 13:00

The Cerny conjecture, concerned with the minimal length of a reset word in a finite automata, is considered one of the most longstanding open problem in the theory of finite automata. ​In this talk, w​e ​discuss​ ​the background of the conjecture, attempts at a proof, and partial results obtained so far by various researchers. In the second part, we present our recent results, which shade a light on the question of why the conjecture is so hard to prove.

Barak Weiss (TAU)
22/03/2015 - 12:00 - 13:00

Suppose a light source is placed in a polygonal hall of mirrors (so light can bounce off the walls). Does every point in the room get illuminated? This elementary geometrical question was open from the 1950s until Tokarsky (1995) found an example of a polygonal room in which there are two points which do not illuminate each other. Resolving a conjecture of Hubert-Schmoll-Troubetzkoy, in joint work with Lelievre and Monteil we prove that if the angles between walls is rational, every point illuminates all but at most finitely many other points. The proof is based on recent work by Eskin, Mirzakhani and Mohammadi in the ergodic theory of the SL(2,R) action on the moduli space of translation surfaces. The talk will serve as a gentle introduction to the amazing results of Eskin, Mirzakhani and Mohammadi.

Valdimir Berkovich
15/03/2015 - 12:00 - 13:00

Non-Archimedean analytic geometry is an analog of complex analytic geometry over non-Archimedean (e.g., p-adic) fields. In the talk, I'll explain what non-Archimedean analytic spaces are, list basic facts about them, and tell about their applications

Pedro V. Silva (University of Porto)
08/03/2015 - 12:00 - 13:00

Hyperbolic groups can be defined through the geometry of Cayley graphs, viewed as geodesic metric spaces. One important feature of hyperbolic groups is the concept of boundary, which can be defined through the topological completion for an appropriate metric (such as the visual metrics), and has the advantages of compactness. An endomorphism of a hyperbolic group admits a continuous extension to the boundary if and only if it is uniformly continuous with respect to a visual metric, and a Hölder condition is a particularly nice way of achieving uniform continuity. In joint work with Vítor Araújo (Universidade Federal da Bahia), we have proved that an endomorphism of a hyperbolic group satisfies a Hölder condition with respect to a visual metric if and only if it is virtually injective and its image is a quasi-convex subgroup. Moreover, if the group is virtually free or torsion-free co-hopfian, then the endomorphism is uniformly continuous if and only if it satisfies a Hölder condition if and only if it is virtually injective. However, this stronger claim does not necessarily hold for arbitrary hyperbolic groups.

Remi Coulon
25/01/2015 - 12:00 - 13:00
The free Burnside group of exponent n, B(r,n), is the quotient of the free group of rank r by the subgroup generated by all n-th powers. This group was introduced in 1902 by W. Burnside who asked whether it is finite or not. This problem motivated many developments in group theory. In 1968 P.S. Novikov and S.I. Adian made a breakthrough by proving that if n is sufficiently large then B(r,n) is infinite. In this talk we will focus on the symmetries of B(r,n). More precisely we will consider on the outer automomorphism group of B(r,n). Among other things, we will see that it inherits some properties coming from the outer automorphism group of free groups.
 
 
Yoram Luzon
18/01/2015 - 12:00 - 13:00

Cooperative interactions, their stability and evolution, provide an interesting context in which to study the interface between cellular and population levels of organization. Such interactions also open the way for the discovery of new population dynamics mechanisms.

We have studied a version of the public goods model relevant to microorganism populations actively extracting a growth resource from their environment. Cells can display one of two phenotypes – a productive phenotype that extracts the resources at a cost, and a non-productive phenotype that only consumes the same resource. We analyze the continuous differential equation model as well as simulate stochastically the full dynamics. It is found that the two sub-populations, which cannot coexist in a well-mixed environment, develop spatio-temporal patterns that enable long-term coexistence in the shared environment. These patterns are solely fluctuation-driven, since the continuous system does not display Turing instability. The average stability of the coexistence patterns derives from a dynamic mechanism in which one sub-population holds the environmental resource close to an extinction transition of the other, causing it to constantly hover around its critical transition point, forming a mechanism reminiscent of selforganized criticality. Accordingly, power-law distributions and long-range correlations are found.

When a time scale separation occurs between two dynamic parameters is defined, a structurally unstable point emerges and any small perturbation of the dynamics with additive noise leads to an equilibrium distribution in which both species coexist in context of additive but not multiplicative noise.

Roman Polyak
11/01/2015 - 12:00 - 13:00

 For three quarters of a century Linear Programming (LP) was the main tool for solving resource allocation problems (RAP)- one of the main problem in economics.

 

 

In 1975 L. V. Kantorovich and T. C. Koopmans shared the Nobel Prize in Economics Nonlinear Equilibrium vs. Linear Programming for resource allocation problems.“for their contributions to the theory of optimum allocation of limited resources."

When LP is used for RAP the prices for goods and the resource availability are given a priori and independent on the production output and prices for the resources. It often leads to solutions, which are not practical, because they contradict to the basic market law of supply and demand.

We consider an alternative to LP approach to RAP, which is based on Nonlinear Equilibrium (NE). The NE is a generalisation of Walras-Wald equilibrium, which is equivalent to J Nash equilibrium in n-person concave game.

NE eliminates the basic drawbacks of LP. Finding NE is equivalent to solving a variation inequality (VI) on the Cartesian product of the primal and dual non negative octants, projection on which is a very simple operation. For solving the VI we consider two methods: projected pseudo-gradient (PPG) and extra pseudo-gradient (EPG), for which projection is the main operation at each step.

We established convergence, proved global Q-linear rate and estimated complexity of both methods under various assumptions on the input data.

Both PPG and EPG can be viewed as pricing mechanisms for establishing economic equilibrium. 

Shifi Reif
04/01/2015 - 12:00 - 13:00
Lie superalgebras and their representations were introduced to mathematics to study supersymmetry in theoretical physics and have since been applicable in algebra, combinatroics, number theory and various other fields.
 
We shall discuss the recently proved Kac-Wakimoto character formula for representations of Lie superalgebras and its specializations to formulas in combinatorics and number theory such as the Jacobi formula for counting the number of presentations of an integer as a sum of k squares.
Zalman Balanov (UT at Dallas)
28/12/2014 - 12:00 - 13:00
The van der Pol oscillator (VDPO) consists of an LCR-contour and a negative feedback loop which can be implemented on the basis of a triode.  The corresponding second order (autonomous)  van der Pol equation is the simplest nonlinear mathematical model widely used in electrical engineering. In practice, one is usually dealing with networks  of  VDPOs coupled symmetrically. Studying the impact of symmetries of a system to the actual dynamics (in particular, symmetric properties and minimal number of periodic regimes) constitutes a problem of great importance and complexity which can be traced back to the classical 16-th Hilbert problem. 
 
Periodic solutions to symmetric autonomous systems very often are studied via the so-called equivariant Hopf bifurcation in a parameterized system (i.e. a phenomenon occurring when the parameter crosses some "critical" value causing a change  of stability of the "trivial solution", which results in appearance of  small amplitude non-constant periodic solutions near the trivial one).  The commonly used method (M. Golubitsky et al.) is based on the equivariant singularity theory (EST) combined with  a Lyapunov-Schmidt reduction or Central Manifold Theorem. However, this method  cannot be applied if the system in question is not smooth enough and/or the phase space does not admit a local linear structure.  
 
On the other hand, if an inductance element in the van der Pol oscillator contains a ferromagnetic core, the ferromagnetic material can introduce a hysteresis relation between the magnetic induction and magnetic field. In many cases (for example, in the presence of the ferroresonance phenomenon), the hysteresis effect cannot be  neglected. As a matter of fact, systems with hysteresis almost always are non-smooth and the corresponding phase spaces do not admit a local linear structure.  Therefore, the EST based method cannot be applied to them. In my talk, I will show how an alternative method based on the usage of the new invariant ‚Äì twisted equivariant degree  (introduced by Z. Balanov and W. Krawcewicz)  -- can be effectively applied to symmetric networks of VDPO with hysteresis. In particular, a direct link between physics, topology, algebra and analysis underlying the VDPOs will be established.
 
This talk is based on a joint work with W. Krawcewicz, D. Rachinskii and A. Zhezherun. 
Dmitry Kerner (BGU)
14/12/2014 - 12:00 - 13:00

Let f be a power series (in several variables) or a C^\infty-smooth function. In many cases just a finite part of Taylor expansion is enough to determine f up to the change of coordinates. Alternatively, the deformations of f by terms of high enough orders are trivial. This phenomenon is called the finite determinacy.
 An immediate application is the algebraization: f has a polynomial representative.

More generally, for maps of smooth spaces the finite determinacy (under various group-actions) has been intensively studied for about 50 years (by Mather, Tougeron, Arnol'd, Wall and many others).
 

Felix Goldberg
07/12/2014 - 12:15 - 13:00

The chip ring game Bjorner, Lovasz and Shor (BLS) introduced the following game in 1991: N chips are placed on the vertices on a n-vertex graph and at every turn, the solitaire player chooses a vertex i of degree di which has at least di chips on it and "fires" i by shifting a chip from i to each of i's neighbours.
The game duration problem BLS have proved the remarkable result that whenever this game terminates, it always does so in the same number of moves, irrespective of gameplay! (I will explain the background for this). They also gave an elegant upper bound on the number of moves. However, computer simulation reveals that the game actually ends in far fewer moves than the BLS bound in all examined cases.
The new results I will show a new approach to obtaining upper bounds on the game duration, based on a re nement of the classic BLS analysis together with a simple but potent new observation.
The new bounds are always at least as good as the BLS bound and in some cases the improvement is dramatic. For example, for the strongly regular graphs BLS reduces to O(nN) while the new bound reduces to O(n+N). For dense regular graphs BLS reduces to O(N) while the new bound reduces to O(n) (for such it holds that n = O(N)).
The proof technique involves a careful analysis of the pseudo-inverse of the graph's discrete Laplacian.
The wider context Time permitting, I will also discuss the appearance of chip ring (and its very close relative, the sandpile model) in diverse mathematical and scientific contexts.

Eli Matzri
30/11/2014 - 12:00 - 13:00

The Inverse Galois Problem, asking which groups can be realizable as
Galois groups of fields, is a major problem in Galois theory.
For example the fact that there is no general formula for the roots of
a polynomial of degree five follows from the fact that
the symmetric group S_5, which is not solvable, is realizable as a
Galois group of a field.
Minac and Tan conjectured that if G is the Galois group of a field,
then G has vanishing triple Massey products (to be defined in the lecture).
In the talk I will give some general background on this new property
and its relation to the inverse Galois problem via a work of Dwyer, and try to give a
flavor of my proof of the Minac-Tan conjecture.

Yair Glasner (BGU)
23/11/2014 - 12:00 - 13:00

Ergodic theory studies actions of a group G by measure preserving transformations on a probability space. Usually the focus is on "essentially free" actions, namely actions for which almost all stabilizers are tirival. Classically the methods are analitic and combinatorial. 

Recently it becomes more and more clear that in the study of non essentially free actions - sophisticated group theoretic tools also come into the picture. I will try to demonstrate this by an array of recent results due to Bader-Lacreux-Duchnese, Tucker-Drob, as well as some joint papers with Abert and Virag and myself.

Joel Hass (UC Davis)
16/11/2014 - 12:00 - 13:00
 
I will talk about recent work showing that the problem of recognizing the 3-sphere lies in the class NP  intersect coNP, assuming the Generalized Riemann Hypothesis.
This is joint work with Greg Kuperberg.
Dr. Nir Lev
23/02/2014 - 12:00

בשעה 11:15 יערך טכס חלוקת הפרסים לזוכים בתחרות  בר-אילן במתמטיקה לסטודנטים 
  
Light refreshments will be served at 11:45 AM next to the Colloquium Room
כיבוד קל יוגש לפני ההרצאה בשעה 11:45 בחדר ע"י חדר המחלקה

The subject of this talk is the analysis of pure point distributions that have a pure point spectrum. 
It will be discussed in the framework of “quasi-crystals" inspired by the experimental discovery in the middle       of the '80s s of non-periodic atomic structures with diffraction patterns consisting of spots. 

Based on joint work with Alexander Olevskii

Anton Khoroshkin
19/01/2014 - 12:00

~~ It is well known that  the generating function of a generic finitely presented algebra is rational.
The purpose of this talk is to present an answer on a similar question in the case of algebraic operads.
 Namely, I will show that the generating series of a generic nonsymmetric operad is an algebraic function
and the generating series of a generic symmetric operad is differentially algebraic.
 Despite the motivation coming from the operad theory, a substantial part of the talk will only deal with the avoidance problems for (labeled) rooted trees hence will be accessible to nonspecialists.

based on  joint work with D.Piontkovsky (arXiv:1202.5170).

Baruch Barzel
12/01/2014 - 12:20

~~One of the major achievements of statistical mechanics is the development of theoretical tools to bridge between the microscopic description of a system and its observed macroscopic behavior, tracking the emergence of large-scale phenomena from the mechanistic description of the system’s interacting components. A key factor in determining this emergent behavior is associated with the underlying geometry of the system’s interactions - a natural notion when treating structured systems, yet difficult to generalize when approaching complex systems. Indeed, social, biological and technological systems feature highly random and non-localized interaction patterns, which challenge the classical connection between structure, dimensionality and dynamics, and hence confront us with a potentially new class of dynamical behaviors. To observe these behaviors we developed a perturbative formalism that enables us to predict an array of pertinent macroscopic functions directly form the microscopic model describing the system’s dynamics. We find that while microscopically complex systems follow diverse rules of interaction, their macroscopic behavior condenses into a discrete set of dynamical universality classes.
Relevant papers:
Universality in network dynamics. Nature Physics 9, 673–681 (2013) doi:10.1038/nphys2741
Network link prediction by global silencing of indirect correlations. Nature Biotechnology 31, 720–725 (2013) doi:10.1038/nbt.2601
 

Yuval Peres
29/12/2013 - 12:00

~~We compare several growth models on the two dimensional lattice. In some models, like internal DLA and rotor-router aggregation, the scaling limits are universal; in particular, starting from a point source yields a disk. In the abelian sandpile, particles are added at the origin and whenever a site has four particles or more, the top four particles topple, with one going to each neighbor. Despite similarities to other models, for the sandpile, the intriguing pattern that arises is not circular and depends on the particular lattice. A scaling limit exists for the sandpile, as was recently shown by Pegden and Smart, but it is not universal and still mysterious. This research has been greatly influenced by pictures of the relevant sets, which I will show in the talk. They suggest a connection to conformal mapping which has not been established yet.
Talk based on joint works with Lionel Levine
 

Chen Meiri
22/12/2013 - 19:25

~~
In this talk we will present a model based on random walks for the density of subsets in finitely generated groups.
The main focus will be on the group large sieve method which is a tool for estimating the density by investigating the finite quotients of the group. We will describe applications of this method for linear groups as well as for mapping class groups.

Ami Viselter
15/12/2013 - 12:00

~~
The concept of group duality is fundamental in the analysis of locally compact abelian groups.
The theory of (analytic) quantum groups was developed in order to provide a framework for duality of general locally compact groups.
The simple set of axioms describing "locally compact quantum groups" (LCQGs) introduced in '00 by Kustermans and Vaes is built on preceding, deep works of Kac and Vainerman, Enock and Schwartz, Woronowicz, Baaj and Skandalis, Masuda and Nakagami and many others.
LCQGs have an intriguing structure theory, and numerous results on locally compact groups have already been generalized to LCQGs.
In this talk we will motivate and introduce the definition of LCQGs, explain and exemplify how they are constructed and mention some of their applications.
Afterwards, we shall describe a generalization of recent work on aspects of ergodic theory of semigroup actions on von Neumann algebras to the context of quantum semigroups.
These results give a Jacobs-de Leeuw-Glicksberg splitting at the von Neumann algebra level.
 

Peter Sternberg
24/11/2013 - 12:00

: I will introduce a variational problem that consists of the classic isoperimetric problem, i.e. minimization of perimeter subject to a volume constraint, perturbed by a nonlocal term modeling long-range interactions. This geometry problem is the focus of much activity these days and I will survey some results of my own and of others aimed at better understanding the rich energy landscape that emerges from the interplay between these two competing terms in the problem.

Serge Itshak Lukasiewicz
17/11/2013 - 12:00

We start with a simple fact: the fundamental solutions of the Laplacian in Rn can be continued as multi-valued

analytic functions in Cn up to the complex bicharacteristic conoid. This extension ramies around the complex

isotropic cone: z2

1 +    z2n

= 0 and has "moderate growth".

For an elliptic linear partial dierential operator of the second order with analytic coe-cients and simple complex characteristics in an open set  Rn, this may be generalized: every fundamental solution can be continued at least locally as a multi-valued analytic function in Cn up to the complex bicharacteristic conoid.

This holomorphic extension is ramied around the bicharacteristic conoid and belongs to the so-called Nilsson

class ("moderate growth").

In fact, those results remain true for such operators with degree bigger than 4 , but the proofs are different due to the lack of natural geodesic distance associated to the operators

Those results may be connected with D-module theory, and more precisely with regular holonomic D-Modules.

We'll explain this link and state a general conjecture

Assaf Rinot
10/11/2013 - 12:00

Paul Cohen showed that the Continuum Hypothesis is independent of the usual axioms of set theory. His solution involved a new apparatus for constructing models of set theory - the method of *forcing*. As Cohen predicted, the method of forcing became very successful in establishing the independence of various statements from the usual axioms of set theory. What Cohen never imagined, is that forcing would be found useful in proving theorems.

In this talk, we shall present a few results in combinatorics whose proof uses the method of forcing, including our recent resolution of the infinite weak Hedetniemi conjecture.

 

The talk will be targeted to a general audience.

Andrei Reznikov
03/11/2013 - 12:00

I will discuss recent progress in the problem of counting nodal domains of eigenfunctions of Laplacian (i.e., counting connected components of the complement to the zero set of  real valued eigenfunctions). This in an old question taken up by Courant and his school. One of many intractable questions is under what conditions one have the number of nodal domains to be unbounded as the eigenvalue goes to infinity. The main difficulty in this problem is that it is known not to be a local property.  
The example I will consider concerns with eigenfunctions of the Laplace-Beltrami operator on compact hyperbolic surfaces. The distinctive property of such a setup is its Quantum (Unique) Ergodicity (to be explained). I will discuss how this could be used in order to deduce strong bounds on eigenfunctions and how this forces the number of nodal domains to grow with the eigenvalue.

(Joint work with J. Bernstein, A. Gosh, P. Sarnak)

Prof. Luis Caffarelli, University of Texas at Austin
14/05/2012 - 13:00

Wolf Prize Day 2012

Prof. Michael Aschbacher, Caltech
14/05/2012 - 11:00

Wolf Prize Day 2012

Gidi Amir
29/04/2012 - 12:00

A central question in the theory of random walks on groups is how symmetries
of the underlying space gives rise to structure and rigidity of the random
walks. For example, for nilpotent groups, it is known that random walks have
diffusive behavior, namely that the rate of escape, defined
as the expected distance of the walk from the identity satisfies
E|Xn|~=n^{1/2}. On nonamenable groups, on the other hand we have E|Xn|
~= n. (~= meaning upto (multiplicative) constants )-


In this work, for every 3/4 <= \beta< 1 we construct a finitely generated
group so that the expected distance of the simple random walk from its
starting point after n steps is n^\beta (up to constants). This answers a
question of Vershik, Naor and Peres. In other examples, the speed exponent can
fluctuate between any two values in this interval.

Previous examples were only of exponents of the form 1-1/2^k or 1 , and were
based on lamplighter (wreath product) constructions.
(Other than the standard beta=1/2 and beta=1 known for a wide variety of groups)
In this lecture we will describe how a variation of the lamplighter
construction, namely the permutational wreath product, can be used to get
precise bounds on the rate of escape in terms of return probabilities of the
random walk on some Schreier graphs. We will then show how groups of
automorphisms of rooted trees, related to automata groups , can then be
constructed and analyzed to get the desired rate of escape.  This is joint
work with Balint Virag of the University of Toronto.
No previous knowledge of randopm walks, automaton groups or wreath products is
assumed.

Reuven Cohen
22/04/2012 - 12:00

Joint work with Sebastian Neumayer, Gil Zussman and Eytan Modiano

Communication networks are vulnerable to natural
disasters, such as earthquakes or floods, as well as to physical
attacks, such as an Electromagnetic Pulse (EMP) attack. Such
real-world events happen in specific geographical locations and
disrupt specific parts of the network. Therefore, the geographical
layout of the network determines the impact of such events on
the network's connectivity. Thus, it is desirable to assess
the vulnerability of geographical networks to such disasters.
I will discuss several algorithms, based on mixed
linear planning and computational geometry, to locate such
vulnerabilities, and present some case studies on real networks.

Ronen Peretz, Ben Gurion University
01/04/2012 - 12:00 - 13:00

The  Jacobian conjecture is a famous open problem in affine algebraic geometry which says

that a polynomial mapping in n complex variables with constant non zero determinant is injective

and surjective witha polynomial inverse mapping.

In this talk we will outline a proof of the surjectivity for the case of n=2 An abstract is attached

 

Prof. E. Leuzinger, Institute for Algebra and Geometry KIT, Germany
18/03/2012 - 12:00

A group $\Gamma$ if of type $F_k$ if it admits an
Eilenberg MacLane complex with finite k-skeleton.
For such groups one can define the (k-1)-dimensional Dehn function,
which measures the difficulty to fill (k-1)-cycles by k-chains.
 I will describe the optimal higher-dimensional Dehn functions for uniform
 S-arithmetic subgroups of reductive groups over global fields.
 I will also discuss a conjectural picture for non-uniform S-arithmetic
 groups.

Steve Gelbart, Weizmann Institute
04/03/2012 - 12:00

The Riemann Zeta-Function is simple to define but utterly
impossible to find all its zeros. Euler looked at it a century before
Riemann to study the prime numbers and the value of the zeta function at the
integers. By 1860, many far-reaching mysteries were uncovered.
We shall describe them, as well as today's Conjectures of Langlands
and Iwasawa which are built upon them.