Fri, 13 May 2022

16:00 - 17:00
N4.01

The Supersymmetric Index and its Holographic Interpretation

Ohad Mamroud
(Weizmann Institute)
Further Information

It is possible to also join online via Microsoft Teams.

Abstract

I'll review 2104.13932, where we analyze the supersymmetric index of N=4 SU(N) Super Yang-Mills using the Bethe Ansatz approach, expressing it as a sum and concentrating on some family of contributions to the sum. We show that in the large N limit each term in this family corresponds to the contribution of a different euclidean black hole to the partition function of the dual gravitational theory. By taking into account non-perturbative contributions (wrapped D3-branes), we further show a one to one match between the contributions of the gravitational saddles and this family of contributions to the index, both at the perturbative and non-perturbative levels. I'll end with some new results regarding the Bethe Ansatz expansion and the information one could extract from it.

Tue, 22 May 2018

14:15 - 15:30
L4

g-algebras and the representations of their invariant subrings.

Anthony Joseph
(Weizmann Institute)
Abstract

Let $\mathfrak g$ be a semisimple Lie algebra.  A $\mathfrak g$-algebra is an associative algebra $R$ on which $\mathfrak g$ acts by derivations.  There are several significant examples.  Let $V$ a finite dimensional $\mathfrak g$ module and take  $R=\mathrm{End} V$ or $R=D(V)$ being the ring of derivations on  $V$ . Again take $R=U(\mathfrak g)$.   In all these cases  $ S=U(\mathfrak g)\otimes R$ is again a $\mathfrak g$-algebra.  Finally let $T$ denote the subalgebra of invariants of $S$.
 
For the first choice of $R$ above the representation theory of $T$ can be rather explicitly described in terms of Kazhdan-Lusztig polynomials.  In the second case the simple $T$ modules can be described in terms of the simple $D(V)$ modules.  In the third case it is shown that all simple $T$ modules are finite dimensional, despite the fact that $T$ is not a PI ring,  except for the case $\mathfrak  g =\mathfrak {sl}(2)$.

Tue, 08 Nov 2016
14:15
L4

Decomposition rules for representations of p-adic groups

Max Gurevich
(Weizmann Institute)
Abstract


What are the irreducible constituents of a smooth representation of a p-adic group that is constructed through parabolic induction? In the case of GL_n this is the study of the multiplicative behaviour of irreducible representations in the Bernstein-Zelevinski ring. Strikingly, the same decomposition problem can be reformulated through various Lie-theoretic settings of type A, such as canonical bases in quantum groups, representations of affine Hecke algebras, quantum affine Lie algebras, or more recently, KLR algebras. While partially touching on some of these phenomena, I will present new results on the problem using mostly classical tools. In particular, we will see how introducing a width invariant to an irreducible representation can circumvent the complexity involved in computations of Kazhdan-Lusztig polynomials.

Fri, 18 Sep 2015
14:00
L4

Post-Snowden Cryptography

Adi Shamir
(Weizmann Institute)
Abstract

Recently, a series of unprecedented leaks by Edward Snowden had made it possible for the first time to get a glimpse into the actual capabilities and limitations of the techniques used by the NSA and GCHQ to eavesdrop to computers and other communication devices. In this talk, I will survey some of the things we have learned, and discuss possible countermeasures against these capabilities.

Tue, 03 Jun 2014

17:00 - 18:00
C5

Counting commensurability classes of hyperbolic manifolds

Tsachik Gelander
(Weizmann Institute)
Abstract

Gromov and Piatetski-Shapiro proved the existence of finite volume non-arithmetic hyperbolic manifolds of any given dimension. In dimension four and higher, we show that there are about $v^v$ such manifolds of volume at most $v$, considered up to commensurability. Since the number of arithmetic ones tends to be polynomial, almost all hyperbolic manifolds are non-arithmetic in an appropriate sense. Moreover, by restricting attention to non-compact manifolds, our result implies the same growth type for the number of quasi- isometry classes of lattices in $SO(n,1)$. Our method involves a geometric graph-of-spaces construction that relies on arithmetic properties of certain quadratic forms.

A joint work with Arie Levit.

Mon, 05 Mar 2012

12:00 - 13:00
L3

Three-sphere partition function, counterterms and supergravity

Cyril Closset
(Weizmann Institute)
Abstract

The partition function of 3d N=2 superconformal theories on the

3-sphere can be computed exactly by localization methods. I will explain

some sublteties associated to that important result. As a by-product, this

analysis establishes the so-called F-maximization principle for N=2 SCFTs in

3d: the exact superconformal R-charge maximizes the 3-sphere free energy

F=-log Z.

Fri, 23 Oct 2009
16:30
L2

*My Nonlinear Odyssey : Analytics*, * Simulation & Visualization *

Professor Norm Zabusky
(Weizmann Institute)
Abstract

An overview of the early history of the soliton (1960-1970) and equipartition in nonlinear 1D lattices : From Fermi-Pasta-Ulam to Korteweg de Vries, to Nonlinear Schrodinger*…., and recent developments .

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