A venue for invited and local speakers to present their research on topics surrounding algebraic geometry and number theory, broadly conceived.

The seminar meets on Wednesdays, 15:10-16:25, in -101

2018–19–A meetings

Upcoming Meetings

Date
Title
Speaker
Abstract
Nov 28 TBA Avner Segal (Bar Ilan)
Dec 5 TBA Nadya Gurevich (BGU)
Dec 12 TBA Ilya Tyomkin (BGU)
Dec 19 TBA Kevin Coulembier (University of Sydney)
Dec 26 TBA Vera Serganova (UC Berkeley)
Jan 2 TBA Tomer Schlank (HUJI)

Past Meetings

Date
Title
Speaker
Abstract
Oct 17 “Poles of the Standard L-function and Functorial Lifts for G2” expanded, part I Avner Segal (Bar Ilan)

This is part 1 of the speaker’s talk from last semester, expanded into a two-part series.

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.

Oct 24 Tamagawa Numbers of Linear Algebraic Groups over Function Fields Zev Rosengarten (HUJI)

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.

Oct 31 Poles of the Standard L-function and Functorial Lifts for G2 Avner Segal (Bar Ilan)

This is part 2 of 2 of an expanded version of the speaker’s talk from last semester.

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.

Nov 7 Some Schur-Weyl Dualities Kieran Ryan (Queen Mary University of London)

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.

Nov 14 The Representation Theory of the finite and infinite Temperley-Lieb algebras Stephen Moore (BGU)

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.

Recurring Seminar run by Dr. Ishai Dan-Cohen