Department of

Mathematics


Seminar Calendar
for Math-Physics events the next 12 months of Sunday, January 1, 2017.

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More information on this calendar program is available.
Questions regarding events or the calendar should be directed to Tori Corkery.
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Thursday, January 19, 2017

12:30 pm in 464 Loomis Laboratory,Thursday, January 19, 2017

One-loop Effective Potentials via Quasinormal Modes.

Cindy Keeler (Niels Bohr Institute)

Abstract: We present a method of calculating one-loop effective potentials for quantum fluctuations from quasinormal modes. We will demonstrate the method for a harmonic oscillator and a scalar in De Sitter space. After briefly discussing its application in Anti-de Sitter space, we will speculate on the physical meaning of this mathematical trick as well as its extension to fields with higher spin, to product spaces, and to spaces with non-Dirichlet boundary conditions.

Thursday, February 9, 2017

12:30 pm in 464 Loomis Laboratory,Thursday, February 9, 2017

Anomaly free SO(3), SO(5), and SO(6) gauge theories from F Theory

Mboyo Esole (Northeastern Math)

Abstract: Orthogonal groups in F Theory are delicate to define as they require a condition on the Mordell-Weil group of the generic elliptic fiber to distinguish them from spin groups. Moreover, the orthogonal groups discussed in the literature are SO (7+k) with k>0. In this talk, I will discuss the explicit construction of lower rank orthogonal groups in F Theory, classify their singular fibers and matter content in 4, 5, and 6 dimensional spacetimes. I will also present the details of their uplift from 5 to 6 dimensions, the cancellations of 6 dimensional anomalies and the structure of the Coulomb phases of the five dimensional theory. All this will be presented as an exercise in intersection theory using a new pushforward theorem for Chow rings of blowups.

Thursday, March 9, 2017

12:30 pm in 464 Loomis Laboratory,Thursday, March 9, 2017

Gauged Wess-Zumino actions, equivariant cohomology, and the electromagnetic response of symmetry-protected topological phases

Matthew Lapa (Illinois Physics)

Abstract: I will introduce the notion of a symmetry-protected topological (SPT) phase protected by the symmetry of a group G, and then present a calculation of the electromagnetic response of some bosonic SPT phases with G=U(1) in all dimensions. Remarkably, we find that the magnitude of the response of these bosonic SPT phases in spacetime dimensions 2m-1 or 2m differs from that of their more familiar fermionic counterparts by a numerical factor of m!, in agreement with previous results in low dimensions. The calculation uses a description of an SPT phase in terms of a nonlinear sigma model (NLSM) with theta term for the bulk and Wess-Zumino term for the boundary. The target space of the NLSM is a sphere of a particular dimension, and a crucial part of the NLSM description is an action of the group G=U(1) on the target space. I will show that the bulk response of the SPT phase can be deduced from the form of the gauged Wess-Zumino action describing the boundary coupled to the electromagnetic field. The construction of the gauged Wess-Zumino action is related to the U(1)-equivariant cohomology of the sphere, and I will explain this connection in detail. In particular, for even-dimensional spheres our result is equivalent to an equivariant extension of the volume form on the sphere with respect to the U(1) symmetry. On the other hand, for odd-dimensional spheres our result gives a physical interpretation for why such an extension fails. This talk is based on the paper arXiv:1611.03504 written together with Chao-Ming Jian, Peng Ye, and Taylor L. Hughes.

Thursday, March 16, 2017

12:30 pm in 464 Loomis Laboratory,Thursday, March 16, 2017

Quivers, Monopoles and q-geometric Langlands

Vasily Pestun (IHES)

Abstract: I will present the relationship between N=2 4d quiver gauge theories and integrable system of periodic monopoles and its quantization, and some conjectures concerning q-deformation of the geometric Langlands correspondence.

Thursday, March 30, 2017

12:30 pm in 464 Loomis Laboratory,Thursday, March 30, 2017

Non-local Virasoro algebras

Gabriele La Nave (Illinois Math)

Abstract: In recent years there have been various proposals explaining physical phenomena via the use of more or less explicitly non-local actions. This is the case of the recent work Guillou-Nunez-Schaposnik on 3-dimensional Bosonization or in the (mostly phenomenological) proposal of Hartnoll and Karch on the strange metal, where they hypothesize the presence of an anomalous dimension for the vector potential. The natural question that arises is to what extent can one construct generalization of the Virasoro algebra that accommodate for the needs of non-local operators. P. Phillips and I in recent work construct such generalizations, thus providing a mathematical foundation for the quest of such non-local CFT's.

Thursday, April 6, 2017

12:30 pm in 464 Loomis Laboratory,Thursday, April 6, 2017

CANCELLED

Anatoly Dymarski (Kentucky Physics)

Thursday, April 13, 2017

12:30 pm in 464 Loomis Laboratory,Thursday, April 13, 2017

Toward classification of 5d SQFTs

Hee-Cheol Kim (Harvard Physics)

Abstract: Non-trivial 5d SUSY theories can be engineered in string theory by using brane constructions or M-theory compactification on CY3. Such theories have interacting UV fixed points. We propose a systematic way to classify non-trivial 5d gauge theories by extending the previous attempt by Intriligator, Morrison and Seiberg. We will present the full classification of 5d gauge theories with simple gauge groups which flow to non-trivial fixed points.

Friday, April 14, 2017

3:00 pm in 141 Altgeld Hall,Friday, April 14, 2017

Some applications of the BV-BFV formalism on manifolds with boundary

Alberto Cattaneo (University of Zurich)

Abstract: According to Segal and Atiyah, a quantum field theory on manifolds with boundary should be thought of as, roughly speaking, the assignment of a vector space (space of states) to the boundary and an element thereof (the state or the evolution operator) to the bulk, in a way that is compatible with gluing. In this talk (based on joint work with P. Mnev and N. Reshetikhin) I will describe how this has to be reformulated when working in perturbation theory. In particular, I will discuss the perturbative quantization of gauge theories on manifolds with boundary. It turns out that, under suitable assumptions, the bulk symmetries, treated in the BV formalism, naturally give rise to a cohomological description of the reduced phase space (BFV formalism) in a correlated way that can be quantized.

Thursday, April 20, 2017

12:30 pm in 464 Loomis Laboratory,Thursday, April 20, 2017

Bulk locality from modular flow

Aitor Lewkowycz (Stanford Physics)

Thursday, April 27, 2017

12:30 pm in 464 Loomis Laboratory,Thursday, April 27, 2017

Entanglement branes in a two-dimensional string theory

Gabriel Wong (Virginia Physics)

Abstract: There is an emerging viewpoint that classical spacetime emerges from highly entangled states of more fundamental constituents. In the context of AdS/CFT, these fundamental constituents are strings, with a dual description as a large-N gauge theory. To understand entanglement in string theory, we consider the simpler context of two-dimensional large-N Yang-Mills theory, and its dual string theory description due to Gross and Taylor. We will show how entanglement in the gauge theory is described in terms of the string theory as thermal entropy of open strings whose endpoints are anchored on a stretched entangling surface which we call an entanglement brane.