AGNT, בן-גוריוןמתמטיקה, בן-גוריון<span class="mathjax">Avner Segal: ”Poles of the Standard L-function and Functorial Lifts for G2“ expanded, part I</span>אוקטובר 17, 15:10—16:25, 2018, -1012018-10-12T09:43:12+03:002018-10-12T09:43:08+03:00מתמטיקה, בן-גוריוןAvner Segalhttps://scholar.google.ca/citations?user=fSSRIIAAAAAJ&hl=enBar Ilan<div class="mathjax"><p>This is part 1 of the speaker‘s talk from last semester, expanded into a two-part series.</p>
<p>The functoriality conjecture is a key ingredient in the theory of automorphic forms and the Langlands program. Given two reductive groups G and H, the principle of functoriality asserts that a map r:G^->H^ between their dual complex groups should naturally give rise to a map r*:Rep(G)->Rep(H) between their automorphic representations. In this talk, I will describe the idea of functoriality, its connection to L-functions and recent work on weak functorial lifts to the exceptional group of type G_2.</p></div><span class="mathjax">Zev Rosengarten: Tamagawa Numbers of Linear Algebraic Groups over Function Fields</span>אוקטובר 24, 15:10—16:25, 2018, -1012018-10-13T19:41:15+03:002018-10-12T09:45:31+03:00מתמטיקה, בן-גוריוןZev RosengartenHUJI<div class="mathjax"><p>In 1981, Sansuc obtained a formula for Tamagawa numbers of reductive groups over number fields, modulo some then unknown results on the arithmetic of simply connected groups which have since been proven, particularly Weil‘s conjecture on Tamagawa numbers over number fields. One easily deduces that this same formula holds for all linear algebraic groups over number fields. Sansuc‘s method still works to treat reductive groups in the function field setting, thanks to the recent resolution of Weil‘s conjecture in the function field setting by Lurie and Gaitsgory. However, due to the imperfection of function fields, the reductive case is very far from the general one; indeed, Sansuc‘s formula does not hold for all linear algebraic groups over function fields. We give a modification of Sansuc‘s formula that recaptures it in the number field case and also gives a correct answer for pseudo-reductive groups over function fields. The commutative case (which is essential even for the general pseudo-reductive case) is a corollary of a vast generalization of the Poitou-Tate nine-term exact sequence, from finite group schemes to arbitrary affine commutative group schemes of finite type. Unfortunately, there appears to be no simple formula in general for Tamagawa numbers of linear algebraic groups over function fields beyond the commutative and pseudo-reductive cases. Time permitting, we may discuss some examples of non-commutative unipotent groups over function fields whose Tamagawa numbers (and relatedly, Tate-Shafarevich sets) exhibit various types of pathological behavior.</p></div><span class="mathjax">Avner Segal: Poles of the Standard L-function and Functorial Lifts for G2</span>אוקטובר 31, 15:10—16:25, 2018, -1012018-10-13T19:39:43+03:002018-10-12T09:58:02+03:00מתמטיקה, בן-גוריוןAvner Segalhttps://scholar.google.ca/citations?user=fSSRIIAAAAAJ&hl=enBar Ilan<div class="mathjax"><p>This is part 2 of 2 of an expanded version of the speaker‘s talk from last semester.</p>
<p>The functoriality conjecture is a key ingredient in the theory of automorphic forms and the Langlands program. Given two reductive groups G and H, the principle of functoriality asserts that a map r:G^->H^ between their dual complex groups should naturally give rise to a map r*:Rep(G)->Rep(H) between their automorphic representations. In this talk, I will describe the idea of functoriality, its connection to L-functions and recent work on weak functorial lifts to the exceptional group of type G_2.</p></div><span class="mathjax">Kieran Ryan: Some Schur-Weyl Dualities</span>נובמבר 7, 15:10—16:25, 2018, -1012018-11-05T13:26:49+02:002018-11-05T13:26:36+02:00מתמטיקה, בן-גוריוןKieran RyanQueen Mary University of London<div class="mathjax"><p>Schur-Weyl Duality is a remarkable theorem giving an intimate link between the representation theories of the Symmetric group S_n, and the General Linear group GL(k). Such a link also holds between other objects, in particular the Brauer Algebra and the Orthogonal group, and the Walled Brauer algebra and GL(k). I will give an introduction to these relationships.</p></div><span class="mathjax">Stephen Moore: The Representation Theory of the finite and infinite Temperley-Lieb algebras</span>נובמבר 14, 15:10—16:25, 2018, -1012018-11-08T17:22:05+02:002018-11-08T16:06:44+02:00מתמטיקה, בן-גוריוןStephen MooreBGU<div class="mathjax"><p>The Temperley-Lieb algebras are a family of finite dimensional algebras that are quotients of the symmetric groups algebras, or more generally the Iwahori-Hecke algebras. They appear in a number of areas of mathematics, including statistical mechanics, knot theory, quantum groups, and subfactors. We review their representation theory and give some results on an infinite dimensional generalization.</p></div><span class="mathjax">Avner Segal: Structure of Degenerate Principal Series of Exceptional Groups</span>נובמבר 28, 15:10—16:25, 2018, -1012018-11-22T12:27:40+02:002018-10-25T12:19:04+03:00מתמטיקה, בן-גוריוןAvner Segalhttp://www.segalavner.comBar Ilan<div class="mathjax"><p>The reducibility and structure of parabolic inductions is a basic problem in the representation theory of p-adic groups. Of particular interest is its principal series and degenerate principal series representations, that is parabolic induction of 1-dimensional representations of Levi subgroups. In this talk, I will start by describing the functor of normalized induction and its left adjoint the Jacquet functor and by going through several examples in the group SL_4(Q_p) will describe an algorithm which can be used to determine reducibility of such representations. This algorithm is the core of a joint project with Hezi Halawi, in which we study the structure of degenerate principal series of exceptional groups of type En (see https://arxiv.org/abs/1811.02974).</p></div><span class="mathjax">Nadya Gurevich : The Zoo of Integral Representations for L-functions</span>דצמבר 5, 15:10—16:25, 2018, -1012018-12-02T15:51:25+02:002018-10-11T12:48:36+03:00מתמטיקה, בן-גוריוןNadya Gurevich https://www.math.bgu.ac.il/~ngur/BGU<div class="mathjax"><p>Automorphic L-functions, initially defined on some right half plane, are conjectured to be have
meromorphic continuation to the whole complex plane. An effective method to prove this in some cases is by using an integral representation. Since the 1960‘s, many such integrals were discovered, some of them representing the same L-function, but seemingly unrelated. Using recent discoveries of D.Ginzburg and D. Soudry, I will explain the relation between different integrals representing the same L-function.</p></div><span class="mathjax">Ilya Tyomkin: Tropicalizations, tropical reductions and liftings of curves with differentials</span>דצמבר 12, 15:10—16:25, 2018, -1012018-12-09T15:29:47+02:002018-10-13T19:36:47+03:00מתמטיקה, בן-גוריוןIlya Tyomkinhttps://ilyatyomkin.wixsite.com/mathBGU<div class="mathjax"><p>Tropicalizations and tropical reductions provide a convenient tool to control degenerations of algebraic objects. Roughly speaking, a tropicalization is a piecewise linear object, associated to an algebraic object over a non-Archimedean field, that contains essential information about one of its integral models. The tropical reduction is then the reduction of the model over the residue field. For applications, it is often important not only to describe the tropicalization process, but also to be able to decide whether something that looks like the tropicalization and the tropical reduction comes from an algebraic object. Such statements are called lifting theorems.
Tropical techniques have been applied successfully to a number of problems in algebraic geometry, such as enumerative questions, dimension estimates, descriptions of compactifications etc. In particular, in a recent work of Bainbridge, Chen, Gendron, Grushevsky, and Moeller, a tropical approach was used to describe a new compactification of the space of smooth curves with differentials (although the authors don’t use this terminology). The proofs of BCGGM rely on transcendental techniques.
In my talk, I will present a modified version of BCGGM tropicalization, and will indicate an algebraic proof of the main result. The talk is based on a joint work with M.Temkin.</p></div><span class="mathjax">Kevin Coulembier: Tensor categories in positive characteristic</span>דצמבר 19, 15:10—16:25, 2018, -1012018-12-13T09:49:28+02:002018-10-09T10:21:34+03:00מתמטיקה, בן-גוריוןKevin Coulembierhttp://www.maths.usyd.edu.au/u/kevinc/University of Sydney<div class="mathjax"><p>Tensor categories are abelian k-linear monoidal categories modeled on the representation categories of affine (super)group schemes over k. Deligne gave very succinct intrinsic criteria for a tensor category to be equivalent to such a representation category, over fields k of characteristic zero. These descriptions are known to fail badly in prime characteristics. In this talk, I will present analogues in prime characteristic of these intrinsic criteria. Time permitting, I will comment on the link with a recent conjecture of V. Ostrik which aims to extend Deligne’s work in a different direction.</p></div><span class="mathjax">Vera Serganova : Support varieties for supergroups</span>דצמבר 26, 15:10—16:25, 2018, -1012018-12-25T16:42:06+02:002018-10-09T10:25:48+03:00מתמטיקה, בן-גוריוןVera Serganova https://math.berkeley.edu/people/faculty/vera-serganovaUC Berkeley<div class="mathjax"><p>We define a functor from the category of representations of algebraic supergroups with reductive even part to the category of equivariant sheaves and show several applications of this construction to representation theory.</p></div><span class="mathjax">Tomer Schlank: Ambidexterity in the T(n)-Local Stable Homotopy Theory</span>ינואר 2, 15:10—16:25, 2019, -1012019-01-01T12:08:40+02:002018-10-16T10:35:08+03:00מתמטיקה, בן-גוריוןTomer Schlankhttps://mathematics.huji.ac.il/people/tomer-schlankHUJI<div class="mathjax"><p>The monochromatic layers of the chromatic
filtration on spectra, that is the K(n)-local (stable 00-)categories Sp_{K(n)} enjoy many remarkable properties. One example is the vanishing of the Tate construction due to Hovey-Greenlees-Sadofsky. The vanishing of the Tate construction can be considered as a natural equivalence between the colimits and limits in Sp_{K(n)} parametrized by finite groupoids. Hopkins and Lurie proved a generalization of this result where finite groupoids are replaced by arbitrary \pi-finite 00-groupoids.</p>
<p>There is another possible sequence of (stable 00-)categories who can be considered as ”monochromatic layers“, those are the T(n)-local 00-categories Sp_{T(n)}. For the Sp_{T(n)} the vanishing of the Tate construction was proved by Kuhn. We shall prove that the analog of Hopkins and Lurie‘s result in for Sp_{T(n)}. Our proof will also give an alternative proof for the K(n)-local case.</p>
<p>This is a joint work with Shachar Carmeli and Lior Yanovski</p></div><span class="mathjax">Saurabh Singh: Reconstruction of formal schemes using their derived categories</span>ינואר 9, 15:10—16:25, 2019, -1012019-05-02T17:03:13+03:002018-11-27T08:48:59+02:00מתמטיקה, בן-גוריוןSaurabh SinghBGU<span class="mathjax">Magnus Carlson: Chern-Simons theory for number fields.</span>מאי 1, 15:10—16:25, 2019, -1012019-04-30T09:52:04+03:002019-04-30T09:52:04+03:00מתמטיקה, בן-גוריוןMagnus CarlsonHUJI<div class="mathjax"><p>In a series of recent papers, Minhyong Kim defined an arithmetic analogue of topological Chern-Simons theory. In this talk, I will introduce this arithmetic Chern-Simons theory and then explain how to compute the arithmetic Chern-Simons invariant for finite, cyclic gauge groups. I will then give some recent applications of these computations.</p>
<p>My work in this talk is based on joint works with Tomer Schlank and Eric Ahlquist.</p></div><span class="mathjax">Mattia Ornaghi : תב“ה</span>מאי 6, 15:10—16:25, 2019, -1012019-05-01T18:20:21+03:002019-04-30T10:22:09+03:00מתמטיקה, בן-גוריוןMattia Ornaghi <span class="mathjax">No Meeting: תב“ה</span>מאי 8, 15:10—16:25, 2019, -1012019-04-30T09:53:26+03:002019-04-30T09:53:26+03:00מתמטיקה, בן-גוריוןNo Meeting<span class="mathjax">Yakov Varshavsky: Perverse sheaves on certain infinite-dimensional spaces, and affine Springer theory</span>מאי 15, 15:10—16:25, 2019, -1012019-05-13T22:23:08+03:002019-04-30T09:55:09+03:00מתמטיקה, בן-גוריוןYakov Varshavskyhttps://mathematics.huji.ac.il/people/yakov-varshavskyHUJI<div class="mathjax"><p>A classical Springer theory is an important ingredient in the classification
of representations of finite groups of Lie type, completed by Lusztig.</p>
<p>The first result of this theory is the assertion that the so-called Grothendieck-Springer sheaf
is perverse and is equipped with an action of the Weyl group. Our main result asserts that an
analogous result also holds in the affine (infinite-dimensional) case.</p>
<p>In the first of my talk I will recall what are perverse sheaves, and why the Grothendieck-Springer
sheaf is perverse. In the rest of the talk I will outline how to extend all this to the affine setting.</p>
<p>We believe that this should have applications to the representations theory of p-adic groups.</p>
<p>This is a joint work with Alexis Bouthier and David Kazhdan</p></div><span class="mathjax">Sergey Fomin: Morsifications and mutations</span>מאי 22, 15:10—16:25, 2019, -1012019-05-15T11:17:43+03:002019-04-30T10:18:34+03:00מתמטיקה, בן-גוריוןSergey Fominhttp://www.math.lsa.umich.edu/~fomin/University of Michigan<div class="mathjax"><p>I will discuss a somewhat mysterious connection between singularity theory and cluster algebras, more specifically between the topology of isolated singularities of plane curves and the mutation equivalence of quivers associated with their morsifications. The talk will assume no prior knowledge of any of these topics. This is joint work with Pavlo Pylyavskyy, Eugenii Shustin, and Dylan Thurston.</p></div><span class="mathjax">Liran Shaul: תב“ה</span>מאי 29, 15:10—16:25, 2019, -1012019-05-01T18:21:54+03:002019-05-01T18:21:54+03:00מתמטיקה, בן-גוריוןLiran Shaulhttps://liranshaul.wordpress.com/Charles University, Prague<span class="mathjax">Dan Edidin: A GIT characterization of cofree representations</span>יוני 5, 15:10—16:25, 2019, -1012019-05-07T20:22:48+03:002019-04-30T10:24:21+03:00מתמטיקה, בן-גוריוןDan Edidinhttps://faculty.missouri.edu/~edidind/University of Missouri, Columbia<div class="mathjax"><p>Let $V$ be a representation of a connected reductive group $G$. A representation is cofree if $k[V]$ is a free $k[V]^G$ module. There is a long history of work studying and classifying cofree representations of reductive groups. In this talk I present a simple conjectural characterization of cofree representations in terms of geometric invariant theory. Matt Satriano and I have proved the conjecture for irreducible representations of SL_n as well as for torus actions. I will give motiviation for the conjecture and explain the techniques which can be used for its verification. This talk based on joint work with Matt Satriano.</p></div><span class="mathjax">Mattia Ornaghi : Localizations of the category of A_{\infty}-categories and Internal Homs (Part II).</span>יוני 12, 15:10—16:25, 2019, -1012019-06-11T15:18:46+03:002019-04-30T10:24:41+03:00מתמטיקה, בן-גוריוןMattia Ornaghi HUJI<div class="mathjax"><p>In this second talk we prove that the localizations of the categories of dg categories, of cohomologically unital and strictly unital A_\inftycategories with respect to the corresponding classes of quasi-equivalences are all equivalent. As an application, we give a complete proof of a claim by Kontsevich stating that the category of internal Homs for two dg categories can be described as the category of strictly unital A_\inftyfunctors between them. This is a joint work with Prof. A. Canonaco and Prof. P. Stellari arXiv:1811.07830.</p></div><span class="mathjax">Lior Bary-Soroker: Number Theory in Function Fields.</span>יוני 19, 15:10—16:25, 2019, -1012019-06-16T16:24:10+03:002019-04-30T10:26:43+03:00מתמטיקה, בן-גוריוןLior Bary-Sorokerhttp://www.math.tau.ac.il/~barylior/TAU<div class="mathjax"><p>I will describe recent threads in the study of number theory in function fields, the different techniques that are used, the challenges, and if time permits the applications of the theory to other subjects such as probabilistic Galois theory.</p></div><span class="mathjax">David Jarossay: Computation of p-adic multiple zeta values and motivic Galois theory</span>אוקטובר 30, 15:10—16:25, 2019, -1012019-10-23T11:21:23+03:002019-10-19T17:04:31+03:00מתמטיקה, בן-גוריוןDavid JarossayBGU<div class="mathjax"><p>Multiple zeta values can be written as sums of series and as integrals. Their integral expression makes them into periods of the pro-unipotent fundamental groupoid of $\mathbb{P}^{1} - {0,1,\infty}$. p-Adic multiple zeta values are defined as p-adic analogues of these integrals. We will show how to express them as sums of series, which allows in particular to compute them explicitly.
We will mention the role of finite multiple zeta values defined by Kaneko and Zagier, and of a question asked by Deligne and Goncharov on a relation between the computation of p-adic multiple zeta values and their algebraic properties. To express the results we will introduce new objects in relation with motivic Galois theory of periods.</p></div><span class="mathjax">Alexei Entin: Factorization statistics for restricted polynomial specializations over large finite fields</span>נובמבר 6, 15:10—16:25, 2019, -1012019-11-01T23:53:11+02:002019-10-23T16:04:49+03:00מתמטיקה, בן-גוריוןAlexei Entinhttps://en-exact-sciences.tau.ac.il/profile/aentinTAU<div class="mathjax"><p>For a polynomial <span class="kdmath">$F(t,A_1,...,A_n)$</span> in <span class="kdmath">$\mathbb{F}_p[t,A_1,...,A_n]$</span> (<span class="kdmath">$p$</span> being a prime number) we study the factorization statistics of its specializations <span class="kdmath">$F(t,a_1,...,a_n)$</span> in <span class="kdmath">$\mathbb{F}_p[t]$</span> with <span class="kdmath">$(a_1,...,a_n) \in S$</span>, where <span class="kdmath">$S=I_1\times\dots\times I_n\subset\mathbb{F}_{p^n}$</span> is a box, in the limit <span class="kdmath">$p\rightarrow\infty$</span> and <span class="kdmath">$deg(F)$</span> fixed. We show that under certain fairly general assumptions on <span class="kdmath">$F$</span>, and assuming that the box dimensions grow to infinity with one of them growing faster than <span class="kdmath">$p^{1/2}$</span>, the degrees of the irreducible factors of <span class="kdmath">$F(t,a_1, \dots,a_n)$</span> are distributed like the cycle lengths of a random permutation in <span class="kdmath">$S_n$</span>.</p>
<p>This improves and generalizes previous results of Shparlinski and more recent results of Kurlberg-Rosenzweig, which in turn generalize the classical Polya-Vinogradov estimate of the number of quadratic residues in an interval.</p></div><span class="mathjax">Sara Tukachinsky: Enumerating pseudoholomorphic curves with boundary</span>נובמבר 13, 15:10—16:25, 2019, -1012019-10-26T16:49:46+03:002019-10-06T12:24:43+03:00מתמטיקה, בן-גוריוןSara Tukachinskyhttp://www.math.ias.edu/~sarabt/IAS<div class="mathjax"><p>Open Gromov-Witten (OGW) invariants should count pseudoholomorphic maps from curves with boundary to a symplectic manifold, with Lagrangian boundary conditions and various constraints on boundary and interior marked points. The presence of boundary of real codimension 1 poses an obstacle to invariance. In a joint work with J. Solomon (2016-2017), we defined genus zero OGW invariants under cohomological conditions. The construction is rather abstract. Nonetheless, in a recent work, also joint with J. Solomon, we find that the generating function of OGW has many properties that enable explicit calculations. Most notably, it satisfies a system of PDE called open WDVV (Witten-Dijkgraaf-Verlinde-Verlinde) equation. For the projective space, this PDE generates recursion relations that allow the computation of all invariants. Furthermore, the open WDVV can be reinterpreted as an associativity of a suitable version of a quantum product.</p>
<p>No prior knowledge of any of the above notions will be assumed.</p></div><span class="mathjax">Haldun Özgür Bayindir : DGAs with polynomial homology</span>נובמבר 20, 15:10—16:25, 2019, -1012019-11-18T17:04:44+02:002019-10-20T10:53:29+03:00מתמטיקה, בן-גוריוןHaldun Özgür Bayindir https://sites.google.com/view/ozgurbayindir/homeHaifa<div class="mathjax"><p>Differential graded algebras(DGAs) are one of the most important
objects of study in homological algebra. These are chain complexes
with an associative and unital multiplication. Examples of DGAs
include cochain complexes of topological spaces equipped with the cup
product.</p>
<p>In this talk, I present our recent classification results on DGAs with
polynomial homology. These results are obtained by exploiting
interesting interactions between DGAs and stable homotopy theory. I am
going to start my talk by stating these classification results. For
the rest of the talk, I am going to present how stable homotopy theory
comes into play for the classification of DGAs. This presentation is
going to be accessible to a general audience.</p></div><span class="mathjax">Hengfei Lu: The Prasad conjecture</span>נובמבר 27, 15:10—16:25, 2019, -1012019-11-11T17:16:16+02:002019-10-23T11:24:29+03:00מתמטיקה, בן-גוריוןHengfei Luhttp://www.wisdom.weizmann.ac.il/~/hengfei/Weizmann<div class="mathjax"><p>Period Problem is one of the most popular interesting problems in recent years, such as the Gan-Gross-Prasad conjectures. In this talk, we mainly focus on the local period problems, so called the relative Langlands programs. Given a quadratic local field extension E/F and a quasi-split reductive group G defined over F with associated quadratic character <span class="kdmath">$\chi_G$</span>, let <span class="kdmath">$\pi$</span> be an irreducible admissible representation of G(E). Assume the Langlands-Vogan conjecture. Dipendra Prasad uses the enhanced L-parameter of <span class="kdmath">$\pi$</span> to give a precise description for the multiplicity <span class="kdmath">$\dim Hom_{G(F)}(\pi,\chi_G)$</span> if the L-packet <span class="kdmath">$\Pi_\pi$</span> contains a generic representation. Then we can verify this conjecture if G=GSp(4).</p></div><span class="mathjax">Ehud de Shalit : The Loxton - van der Poorten conjecture, and an elliptic analogue</span>דצמבר 4, 15:00—16:15, 2019, -1012019-12-01T21:10:06+02:002019-10-20T10:55:34+03:00מתמטיקה, בן-גוריוןEhud de Shalit http://www.math.huji.ac.il/~deshalit/new_site/default.htmHUJI<div class="mathjax"><p>The conjecture of Loxton and var der Poorten is a criterion for a formal power series
to be the expansion at 0 of a rational function, and is related to a famous theorem of Cobham
in the theory of finite automata. It was proved by Adamczewski and Bell in 2013. Recently,
Schafke and Singer found a novel approach that lead also to a simple conceptual proof of
Cobham‘s theorem. We shall explain these results and the cohomological machinery
behind them, and discuss what is missing from the picture to establish an elliptic analogue.</p></div><span class="mathjax">Ariel Weiss: Irreducibility of Galois representations associated to low weight Siegel modular forms</span>דצמבר 11, 15:00—16:15, 2019, -1012019-12-02T17:42:11+02:002019-10-20T10:59:03+03:00מתמטיקה, בן-גוריוןAriel Weisshttp://ariel-weiss.postgrad.shef.ac.uk/HUJI<div class="mathjax"><p>If f is a cuspidal modular eigenform of weight k>1, Ribet proved that its associated p-adic Galois representation is irreducible for all primes. More generally, it is conjectured that the p-adic Galois representations associated to cuspidal automorphic representations of GL(n) should always be irreducible.</p>
<p>In this talk, I will prove a version of this conjecture for <em>low weight, genus 2 Siegel modular forms</em>. These two-dimensional analogues of weight 1 modular forms are, conjecturally, the automorphic objects that correspond to abelian surfaces.</p></div><span class="mathjax">Amnon Yekutieli: Flatness and Completion Revisited</span>דצמבר 18, 15:00—16:15, 2019, -1012019-12-17T12:38:22+02:002019-10-23T11:26:38+03:00מתמטיקה, בן-גוריוןAmnon Yekutielihttps://www.math.bgu.ac.il/~amyekut/BGU<div class="mathjax"><p>https://www.math.bgu.ac.il/~amyekut/lectures/flat-comp-revis/abstract.html</p></div><span class="mathjax">Nadya Gurevich: Fourier transforms on the basic affine space</span>דצמבר 25, 15:00—16:15, 2019, -1012019-12-23T11:57:27+02:002019-10-20T11:11:58+03:00מתמטיקה, בן-גוריוןNadya Gurevichhttps://www.math.bgu.ac.il/~ngur/BGU<div class="mathjax"><p>For a quasi-split group $G$ over a local field $F$, with Borel subgroup $B=TU$ and Weyl group $W$,
there is a natural geometric action of $G\times T$ on $L^2(X),$ where $X=G/U$ is the basic affine space of $G$.
For split groups, Gelfand and Graev have extended this action to an action of
$G\times (T\rtimes W)$ by generalized Fourier transforms $\Phi_w$. We shall extend this result for quasi-split groups, using a new interpretation
of Fourier transforms for quasi-split groups
of rank one.</p>
<p>This is joint work with David Kazhdan.</p></div><span class="mathjax">Ari Shnidman: Monogenic cubic fields and local obstructions</span>ינואר 1, 15:00—16:15, 2020, -1012019-12-29T18:43:48+02:002019-10-20T11:13:48+03:00מתמטיקה, בן-גוריוןAri Shnidmanhttp://math.huji.ac.il/~shnidman/HUJI<div class="mathjax"><p>A number field is monogenic if its ring of integers is generated by a single element. It is conjectured that 0% of degree d number fields are monogenic (for any d > 2). There are local obstructions that force this proportion to be < 100%, but beyond this very little is known. I‘ll discuss work with Alpoge and Bhargava showing that a positive proportion of cubic fields (d = 3) have no local obstructions and yet are still not monogenic. This uses new results on integral points and ranks of Selmer groups of elliptic curves in twist families.</p></div><span class="mathjax">Ilya Tyomkin: Irreducibility problem for Severi varieties</span>ינואר 8, 15:00—16:15, 2020, -1012020-01-06T17:49:42+02:002019-10-20T11:15:59+03:00מתמטיקה, בן-גוריוןIlya Tyomkinhttps://www.math.bgu.ac.il/en/people/users/christkBGU<div class="mathjax"><p>Severi varieties parameterize reduced irreducible curves of given geometric genus in a given linear system on an algebraic surface. The first irreducibility result for Severi varieties was established in 1986, and it is due to Harris, who considered the classical case of planar curves in characteristic zero. Few more irreducibility results have been obtained since then, but none of the known approaches is applicable in positive characteristic. In my talk, I will discuss the history and the state of the art in the irreducibility problem, and will also announce new results obtained in a joint work with Karl Christ and Xiang He.</p></div><span class="mathjax">Karl Christ: Degenerating plane curves via tropicalization</span>ינואר 15, 15:00—16:15, 2020, -1012020-01-06T17:45:38+02:002019-10-20T11:16:36+03:00מתמטיקה, בן-גוריוןKarl ChristBGU<div class="mathjax"><p>In my talk, I will describe how simultaneous stable reduction and tropical geometry can be used to construct degenerations of plane curves. This is the main ingredient in a new proof for irreducibility of Severi varieties of the projective plane. The crucial feature of this construction is that it works in positive characteristic, where the other known methods fail. The talk will be a follow up on last week‘s talk and is based on joint work with Xiang He and Ilya Tyomkin.</p></div><span class="mathjax">Amnon Yekutieli: Commutative DG Rings and their Derived Categories</span>ינואר 22, 15:00—16:15, 2020, -1012020-01-16T12:10:33+02:002019-10-23T11:27:46+03:00מתמטיקה, בן-גוריוןAmnon Yekutielihttps://www.math.bgu.ac.il/~amyekut/BGU<div class="mathjax"><p>The commutative DG rings in the title are more commonly known as ”nonpositive strongly commutative unital differential graded cochain K-algebras“, where K is a commutative base ring. In the literature the standard assumption is that K is a field of characteristic zero - but one of our themes in this talk is that this assumption is superfluous (K = Z works just as well).</p>
<p>There are two kinds of derived categories ralated to commutative DG rings. First, given a DG ring A, we can consider D(A), the derived category of DG A-modules, which is a K-linear triangulated category. This story is well understood by now, and I will only mention it briefly.</p>
<p>In this talk we shall consider another kind of derived category. Let DGRng denote the category whose objects are the commutative DG rings (the base K is implicit), and whose morphisms are the DG ring homomorphisms. The derived category of commutative DG rings is the category D(DGRng) gotten by inverting all the quasi-isomorphisms in DGRng. (In homotopy theory the convention is to call it the ”homotopy category“, but this is an unfortunate historical accident.)</p>
<p>I will define semi-free DG rings, and prove their existence and lifting properties. Then I will introduce the quasi-homotopy relation on DGRng, giving rise to the quotient category K(DGRng), the ”genuine“ homotopy category. One of the main results is that the canonical functor from K(DGRng) to D(DGRng) is a faithful right Ore localization.</p>
<p>I will conclude with a theorem on the existence of the left derived tensor product inside D(DGRng), and with the pseudofunctor from D(DGRng) to the TrCat, sending a DG ring A to the triangulated category D(A).</p>
<p>Next semester I will talk about the geometrization of these ideas: ”The Derived Category of Sheaves of Commutative DG Rings“.</p></div><span class="mathjax">none: תב“ה</span>אוקטובר 27, 16:00—17:15, 2021, -1012021-10-24T16:15:13+03:002021-10-24T16:11:11+03:00מתמטיקה, בן-גוריוןnone<span class="mathjax">Ariel Weiss: Prime torsion in the Tate-Shafarevich groups of abelian varieties over $\mathbb{Q}$</span>נובמבר 3, 16:00—17:15, 2021, -1012021-10-25T18:44:45+03:002021-10-24T16:10:34+03:00מתמטיקה, בן-גוריוןAriel Weisshttp://www.math.huji.ac.il/~arielweiss/BGU<div class="mathjax"><p>Very little is known about the Tate-Shafarevich groups of abelian varieties. On the one hand, the BSD conjecture predicts that they are finite. On the other hand, heuristics suggest that, for each prime $p$, a positive proportion of elliptic curves $E/\mathbb{Q}$ have $\Sha(E)[p] \ne 0$, and one expects something similar for higher dimensional abelian varieties as well. Yet, despite these expectations, it seems to be an open question whether, for each prime $p$, there exists even a single elliptic curve over $\mathbb{Q}$ with $\Sha(E)[p] \ne 0$. In this talk, I will show that, for each prime $p$, there exists a geometrically simple abelian variety $A/\mathbb{Q}$ with $\Sha(A)[p]\ne 0$. Our examples arise from modular forms with Eisenstein congruences. This is joint work with Ari Shnidman.</p></div><span class="mathjax">Ariyan Javanpeykar: Rational points on ramified covers of abelian varieties, online lecture</span>נובמבר 10, 16:00—17:15, 2021, -1012021-11-08T10:04:19+02:002021-10-24T16:12:28+03:00מתמטיקה, בן-גוריוןAriyan Javanpeykarhttps://www.agtz.mathematik.uni-mainz.de/arakelov-geometrie/junior-prof-dr-ariyan-javanpeykar/Meinz<div class="mathjax"><p>Let X be a ramified cover of an abelian variety A over a number field k. According to Lang‘s conjecture, the k-rational points of X should not be dense. In joint work with Corvaja, Demeio, Lombardo, and Zannier, we prove a slightly weaker statement. Namely, assuming A(k) is dense, we show that the complement of the image of X(k) in A(k) is (still) dense, i.e., there are less points on X than there are on A (or: there are more points on A than on X). In this talk I will explain how our proof relies on interpreting this as a special case of a version of Hilbert‘s irreducibility theorem for abelian varieties.</p></div><span class="mathjax">No talk: תב“ה</span>נובמבר 17, 16:00—17:15, 2021, -1012021-11-17T14:59:22+02:002021-10-24T16:13:34+03:00מתמטיקה, בן-גוריוןNo talk<div class="mathjax"><p><strong>strong text</strong></p></div><span class="mathjax">David Corwin: Quadratic Chabauty and Beyond</span>נובמבר 24, 16:00—17:15, 2021, -1012021-11-22T11:33:52+02:002021-10-24T16:16:10+03:00מתמטיקה, בן-גוריוןDavid Corwinhttps://math.berkeley.edu/~dcorwin/BGU<div class="mathjax"><p>I will describe my work (some joint with I. Dan-Cohen) to extend the computational boundary of Kim‘s non-abelian Chabauty‘s method. Faltings‘ Theorem says that the number of rational points on curves of higher genus is finite, and non-abelian Chabauty provides a blueprint both for proving this finiteness and for computing the sets. We first review classical Chabauty-Coleman, which does the same but works only for certain curves. Then we describe Kim‘s non-abelian generalization, which replaces abelian varieties in Chabauty-Coleman by Selmer groups (a kind of Galois cohomology) and eventually ”non-abelian“ Selmer varieties. Finally, we describe recent work in attempting to compute these sets using the theory of Tannakian categories.</p></div><span class="mathjax">Sa‘ar Zehavi: תב“ה</span>דצמבר 1, 16:00—17:15, 2021, -1012021-10-24T16:17:48+03:002021-10-24T16:17:48+03:00מתמטיקה, בן-גוריוןSa'ar ZehaviTAU<span class="mathjax">David Ter-Borch Gram Lilienfeldt: Experiments with Ceresa classes of cyclic Fermat quotients</span>דצמבר 8, 16:00—17:15, 2021, -1012021-12-06T23:10:50+02:002021-10-25T18:56:45+03:00מתמטיקה, בן-גוריוןDavid Ter-Borch Gram Lilienfeldthttps://math.huji.ac.il/~lilienfeldt/HUJI<div class="mathjax"><p>We give two new examples of non-hyperelliptic curves whose Ceresa cycles have torsion images in the intermediate Jacobian. For one of them, we find that the central value of the L-function of the relevant motive is non-vanishing, consistent with the conjectures of Beilinson and Bloch. We speculate on a possible explanation for the existence of these torsion Ceresa classes, based on some computations with cyclic Fermat quotients. This is joint work with Ari Shnidman.</p></div><span class="mathjax">Dmitry Kerner: Finite determinacy of maps. Group orbits vs the tangent spaces</span>דצמבר 15, 16:00—17:15, 2021, -1012021-12-13T09:45:45+02:002021-10-25T18:57:43+03:00מתמטיקה, בן-גוריוןDmitry Kernerhttps://www.math.bgu.ac.il/~kernerdm/BGU<div class="mathjax"><p>Consider a morphism of germs of Noetherian schemes, f: (X,x)-> (Y,y). When is it ’stable‘ under perturbations by higher order terms? I.e. when can such a perturbation be undone by a group action, e.g. by the local coordinate changes.
This question has been extensively studied for real/complex analytic (or C^k) maps
(k^n,o)-> (k^m,o). The idea is to reduce the orbit study, Gf, to the study of the tangent space, T_G f.
The classical methods used vector field integration and infinite dimensional Lie groups, thus obstructing extensions to the zero/positive characteristic. During the last years we have developed a purely algebraic approach to this problem, extending the results to arbitrary characteristic.
The key tool is the ’Lie-type pair‘. This is a group G, its would-be tangent space T_G, and certain maps between G, T_G, approximating the classical exponential/logarithm.</p>
<p>(joint work with G. Belitskii, A.F. Boix, G.M. Greuel.)</p></div><span class="mathjax">Ido Efrat: Filtrations of profinite groups as intersections and absolute Galois groups</span>דצמבר 22, 16:00—17:15, 2021, -1012021-12-13T09:52:04+02:002021-10-25T18:58:39+03:00מתמטיקה, בן-גוריוןIdo Efrathttps://www.math.bgu.ac.il/~efrat/BGU<div class="mathjax"><p>The general structure of absolute Galois groups of fields as profinite groups is still a mystery. Among the very few
known properties of such groups are several “Intersection Theorems”, describing subgroups in standard filtrations
of absolute Galois groups as the intersection of all normal open subgroups with quotient in a prescribed list of
finite groups. These theorems are based on deep cohomological properties of absolute Galois groups. We will
present a general “Transfer Theorem” for profinite groups, which explains what lies behind these intersection
theorems.</p></div><span class="mathjax">Amit Ophir: תב“ה</span>דצמבר 29, 16:00—17:15, 2021, -1012021-12-06T23:19:19+02:002021-12-06T23:19:19+02:00מתמטיקה, בן-גוריוןAmit OphirHUJI<span class="mathjax">Daniel Disegni: Theta cycles</span>ינואר 5, 16:00—17:15, 2022, -1012022-01-04T10:50:08+02:002021-12-06T23:20:45+02:00מתמטיקה, בן-גוריוןDaniel Disegnihttps://disegni-daniel.perso.math.cnrs.fr/index.htmlBGU<div class="mathjax"><p>I will discuss results and open problems in an emerging theory of ‘canonical’ algebraic cycles for all motives enjoying a certain symmetry. The construction is inspired by theta series, and based on special subvarieties in arithmetic quotients of the complex unit ball.
The ‘theta cycles’ seem as pleasing as Heegner points on elliptic curves: (1) their nontriviality is detected by derivatives of complex or p-adic L-functions; (2) if nontrivial, they generate the Selmer group of the motive. This supports analogues of the Birch and Swinnerton-Dyer conjecture. I will focus on (2), whose proof combines the method of Euler systems and the local theta correspondence in representation theory.</p></div><span class="mathjax">: תב“ה</span>מרץ 2, 16:00—17:15, 2022, -1012021-10-24T16:08:05+03:002021-10-24T16:08:05+03:00מתמטיקה, בן-גוריון