**Title:** Kahler geometry in physics and probability

**Speaker:** Semyon Klevtsov

**Date:** Tuesday, June 16, 2015

**Time:** 1:00pm – 2:00pm

**Place:** Lecture Hall 102, Simons Center

[/box]

**Abstract:** Recent advances in Kahler geometry provide new tools for the analysis of the Quantum Hall effect, for random geometry and for other probabilistic aspects of physics. Electron configurations define singular Kahler metrics on a Riemann surface, with the probability of a configuration defined by the Laughlin state. The statistics of configurations are governed by Kahler geometric functionals. The same Kahler analysis can be used to study the statistics of random smooth Kahler metrics as well. My talk will survey the methods, results and open problems in the area.

**Title:** Open string field theory revisited

**Speaker:** Samson Shatashvili

**Date:** Tuesday, June 09, 2015

**Time:** 01:00pm – 02:00pm

**Place:** Seminar Room 313, Simons Center

[box, type=”download”]Watch the Video.

[/box]

**Abstract:** I discuss the subtleties and open questions concerning the background independent open string field theory (sometimes called BSFT)

**Title:** Solvable Schroedinger equations and representation theory

**Speaker:** Alexander Turbiner, Nuclear Science Institute, National Autonomous University of Mexico

**Date:** Tuesday, May 12, 2015

**Time:** 01:00pm – 02:00pm

**Place:** Lecture Hall 102, Simons Center

[box, type=”download”]Watch the Video.

[/box]

**Abstract:** For any quantum Calogero-Sutherland (CS) Hamiltonian (rational, trigonometric, elliptic) for any root system:

(I) one can indicate a change of variables in which its potential is a rational function and contravariant (flat) metric has polynomial entries;

(II) there exists a similarity transformation (gauge rotation) of the Hamiltonian after which it becomes the 2nd order differential, algebraic operator with polynomial coefficient functions;

(III) the algebraic operator has a finite-dimensional invariant subspace in polynomials which is a representation space of an algebra of differential operators (for $A_n$ and $BC_n$ cases this is the $gl(n+1)$-algebra)

In one-dimensional case ($A_1$ and $BC_1$ CS models) the algebraic operator is the (restricted) Heun operator (for elliptic) and the Riemann operator (for rational and trigonometric).

]]>**Title:** “WHAT IS … F-theory?”

**Speaker:** David Morrison, UC Santa Barbara

**Date:** Tuesday, September 9, 2014

**Time:** 1:00pm – 2:00pm

**Place:** Lecture Hall 102, Simons Center

[box, type=”download”]Watch the video.[/box]

**Abstract:** In the spirit of the “WHAT IS …” series of articles in the Notices of the American Mathematical Society, I will give a description of F-theory from first priniciples. On the one hand, F-theory is a theory of quantum gravity which arose from string theory but which is not exactly part of string theory. (I will explain these things to non-physicists.) On the other hand, F-theory provides a fascinating application of the Weierstrass p-function and the theory of elliptic curves, including the height pairing and the Mordell-Weil and Tate-Shafarevich groups. (I will explain these things to non-mathematicians.)

**Title:** The d-orbifold programme, with applications to moduli spaces of J-holomorphic curves. Overview

**Speaker:** Dominic Joyce, Oxford

**Date:** Tuesday, May 6, 2014

**Time:** 1:00pm-2:00pm

**Place:** Lecture Hall 102, Simons Center

[box, type=”download”]Watch the video.[/box]

]]>

**Title:** Many faces of characters

**Speaker:** Nikita Nekrasov

**Date:** Tuesday, April 29, 2014

**Time:** 1:00pm-2:00pm

**Place:** Lecture Hall 102, Simons Center

[box, type=”download”]Watch the video.[/box]

**Abstract:** In representation theory, a character is a function (distribution) on the group, given roughly by the trace of the group element in the given representation. In physics the character is a partition function in quantum mechanical system with twisted boundary conditions. The famous Weyl and Kac-Weyl character formulae have geometric meaning natural for the quantum mechanical interpretation. I will present the novel approaches to characters and their quantum deformations, inspired by the four dimensional gauge theory and Langlands program.

**Title:** Fractional Quantum Hall Effect on Riemann Surfaces

**Speaker:** Paul Wiegmann, University of Chicago

**Date:** Tuesday, April 22, 2014

**Time:** 1:00pm-2:00pm

**Place:** Lecture Hall 102, Simons Center

[box, type=”download”]Watch the video.[/box]

**Abstract:** Fractional Quantum Hall Effect (FQHE) describes electronic gas in quantizing magnetic field. In realistic setting electrons are confined in a plane. However, many subtle properties of this phenomena are revealed and better understood would electronic liquid be placed on a Riemann surface instead. Then a response of electronic liquid to a change of the geometry (metric) generates sensible physical information. In return FQHE on Riemann surfaces fosters sensible geometric objects and structures yet to be understood.

**Title:** Hamiltonian dynamics of fluids and vortex sheets

**Speaker:** Boris Khesin

**Date:** Tuesday, April 8, 2014

**Time:** 1:00pm-2:00pm

**Place:** Lecture Hall 102, Simons Center

[box, type=”download”]Watch the video. [/box]

**Abstract:** We show that an approximation of the hydrodynamical Euler equation

describes the binormal mean-curvature flow on vortex membranes in any dimension. This generalizes the classical binormal, or vortex filament, equation in 3D. We present a Hamiltonian framework for higher-dimensional vortex filaments and vortex sheets as singular

2-forms with support of codimensions 2 and 1, respectively. This framework, in particular, allows one to define symplectic structures on the spaces of vortex sheets.

[box, type=”download”]Watch the video.

View the Slides.[/box]

**Abstract:** Recently algebraic objects with multivalued operations appeared in different areas. Apparently, multivalued algebraic operations reside in any part of the mathematical universe. The triangle inequality, valuations, tropical varieties, characteristic one, algebraic K-functors are related to multivalued operations. They demonstrate greater flexibility and, in particular, allow deformations, where the univalued operations do not.

The talk will be devoted to the basic notions and examples of multivalued algebra.

]]>

[box, type=”download”]Watch the video.

View the slides.[/box]

**Abstract:** I will review the recent BICEP2 CMB results and put them in context with other CMB experiments. I will also address the robustness of these results and their implications for inflation.