הסמינר מתכנס בימי רביעי, בשעות 15:10-16:30, באולם -101

השבוע


Ran Tessler (ETH)

Integrable hierarchies, wave functions and open intersection theories

I will discuss the KdV integrable hierarchy, and its tau functions and wave functions.

Witten conjectured that the tau functions are the generating functions of intersection numbers over the moduli of curves (now Kontsevich’s theorem). Recently the following was conjectured: The KdV wave function is a generating function of intersection numbers on moduli of “Riemann surfaces with boundary” (Pandharipande-Solomon-T,Solomon-T,Buryak).

I will describe the conjecture, its generalization to all genera (Solomon-Tessler), and sketch its proof (Pandharipande-Solomon-T in genus 0, T,Buryak-T for the general case). If there will be time, I’ll describe a conjectural generalization by Alexandrov-Buryak-T.


מפגשים בסמסטר סתיו 2017

המפגשים הבאים

תאריך
כותרת
מרצה
תקציר
22 בנוב Integrable hierarchies, wave functions and open intersection theories Ran Tessler (ETH)

I will discuss the KdV integrable hierarchy, and its tau functions and wave functions.

Witten conjectured that the tau functions are the generating functions of intersection numbers over the moduli of curves (now Kontsevich’s theorem). Recently the following was conjectured: The KdV wave function is a generating function of intersection numbers on moduli of “Riemann surfaces with boundary” (Pandharipande-Solomon-T,Solomon-T,Buryak).

I will describe the conjecture, its generalization to all genera (Solomon-Tessler), and sketch its proof (Pandharipande-Solomon-T in genus 0, T,Buryak-T for the general case). If there will be time, I’ll describe a conjectural generalization by Alexandrov-Buryak-T.

29 בנוב TBA Lior Yanovski (Hebrew University )
6 בדצמ Purity for big Galois representations Jyoti Prakash Saha (BGU)

In 1980s, Hida constructed p-adic families of ordinary cusp forms. He showed that the Fourier expansions of the ordinary normalized Hecke eigen cusp forms can be p-adically interpolated. Moreover, their associated Galois representations can also be interpolated via a big Galois representation. The Galois representations associated to cusp forms are known to be pure. This suggests a notion of purity for big Galois representations. In this talk, we will discuss this notion and explain its role in the study of variation in p-adic families.

13 בדצמ תב”ה Dmitry Kerner (BGU)
20 בדצמ תב”ה Avner Segal (UBC)
27 בדצמ Algebraic Families of Harish-Chandra Modules and their Application Eyal Subag (Penn State)

I shall review the framework of algebraic families of Harish-Chandra modules, introduced recently, by Bernstein, Higson, and the speaker. Then, I shall describe three of their applications. The first is contraction of representations of Lie groups. Contractions are certain deformations of representations with applications in mathematical physics. The second is the Mackey bijection, this is a (partially conjectural) bijection between the admissible dual of a real reductive group and the admissible dual of its Cartan motion group. The third is the hidden symmetry of the hydrogen atom as an algebraic family of Harish-Chandra modules.

3 בינו תב”ה Shane Kelly (FU Berlin)
10 בינו תב”ה Gennady Lyubeznik (University of Minnesota)

המפגשים הקודמים

תאריך
כותרת
מרצה
תקציר
25 באוק Injective modules in higher algebra Liran Shaul (Ben Gurion University )

Injective modules are fundamental in homological algebra over rings. In this talk, we explain how to generalize this notion to higher algebra. The Bass-Papp theorem states that a ring is left noetherian if and only if an arbitrary direct sum of left injective modules is injective. We will explain a version of this result in higher algebra, which will lead us to the notion of a left noetherian derived ring. In the final part of the talk, we will specialize to commutative noetherian rings in higher algebra, show that the Matlis structure theorem of injective modules holds in this setting, and explain how to deduce from it a generalization of Grothendieck’s local duality theorem over commutative noetherian local DG rings.

1 בנוב Foliations on unitary Shimura varieties in positive characteristic Ehud de Shalit (Hebrew University )

Let E be a quadratic imaginary field and p a prime which is inert in E. Let S be the special fiber (at p) of a unitary Shimura variety of signature (n,m) and hyperspecial level subgroup at p, associated with E/Q.

We study a natural foliation in the tangent bundle of S, which is originally defined on the \mu-ordinary stratum only, but is extended to a certain non-singular blow-up of S. We identify the quotient of S by the foliation with a certain irreducible component of a Shimura variety with parahoric level structure at p. As a result we get new results on the singularities of the latter.

We study integral submanifolds of the foliation and end the talk with a new conjecture of Andre-Oort type.

15 בנוב Non-Semisimple Planar Algebras from Restricted Quantum sl_2 Stephen Moore (BGU)

Planar algebras are a type of diagrammatic graded algebra, introduced to axiomatize the standard invariant of subfactors. The fundamental example is the Temperley-Lieb algebra which can be constructed as End(X^n), where X is a quantum sl_2 module. Recently, there has been interest in a finite dimensional version of quantum sl_2, known as restricted quantum sl_2, and it has been conjectured that its representation theory is equivalent to a logarithmic conformal field theory. We aim to generalize the Temperley-Lieb construction to the restricted case, giving generators and relations of the planar algebra, and describing morphisms between indecomposable modules diagrammatically.

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