Department of

# Mathematics

Seminar Calendar
for Mathematical Physics events the year of Tuesday, August 21, 2018.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
      July 2018             August 2018           September 2018
Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa
1  2  3  4  5  6  7             1  2  3  4                      1
8  9 10 11 12 13 14    5  6  7  8  9 10 11    2  3  4  5  6  7  8
15 16 17 18 19 20 21   12 13 14 15 16 17 18    9 10 11 12 13 14 15
22 23 24 25 26 27 28   19 20 21 22 23 24 25   16 17 18 19 20 21 22
29 30 31               26 27 28 29 30 31      23 24 25 26 27 28 29
30


Monday, April 16, 2018

3:00 pm in 243 Altgeld Hall,Monday, April 16, 2018

#### The globalization of the Poisson sigma model in the BV-BFV formalism

###### Nima Moshayedi (University of Zurich)

Abstract: One of the central problems of mathematical physics is understanding how to pass from classical to quantum physics. One procedure that implements that passage, called deformation quantization, achieves quantization by deforming the Poisson algebra of classical observables into a non-commutative algebra of quantum observables. The algebraic structure of the quantum observables is determined by the star product, which is a formal deformation of the algebraic structure on the classical observables. Kontsevich showed that any Poisson manifold admits a star product and gave an explicit formula for it. The Poisson Sigma Model (PSM) is an AKSZ-theory closely related to deformation quantization. We will give a short introduction to the BV-BFV formalism, the PSM and discuss briefly how we can construct a globalized version of Kontsevich's star product using this formalism by extending a condition called the modi fied Quantum Master Equation to a differential version of it.

Monday, September 10, 2018

2:00 pm in 464 Loomis,Monday, September 10, 2018

#### Aspects, Generalizations, and Applications of the Holographic Entanglement of Purification

###### Ning Bao (UC Berkeley)

Abstract: In this talk, we will define, and motivate the holographic entanglement of purification and several generalizations thereof. We will then make some comments on applications of these quantities in the context of quantum information theory, quantum error correction and bulk reconstruction.

Thursday, September 27, 2018

12:30 pm in 464 Loomis,Thursday, September 27, 2018

#### Hecke Relations in Rational Conformal Field Theory

###### Jeffrey Harvey (U. of Chicago)

Abstract: Hecke operators that act on characters of rational conformal field theories are defined and we use these to show that many characters of different RCFTs are related by Hecke operators. These relations extend the previously studied Galois symmetry of the modular representations appearing in RCFT. Connections with modular linear differential equations will also be discussed.

Thursday, October 4, 2018

12:30 pm in 464 Loomis,Thursday, October 4, 2018

#### To Be Announced

###### Jim Halverson (Northeastern)

Thursday, October 18, 2018

12:30 pm in 464 Loomis,Thursday, October 18, 2018

#### Particle-vortex statistics and the nature of dense quark matter

###### Aleksey Cherman (INT Washington)

Abstract: Dense nuclear matter is expected to be a superfluid. Quark matter, which is expected to appear at higher densities, is also a superfluid. But quark matter turns out to be sharply distinct from a standard superfluid, because it supports Z3-valued particle-vortex braiding phases, and its effective action includes a coupling to a topological quantum field theory. Physically, our results imply that certain mesonic and baryonic excitations have orbital angular momentum quantized in units of ħ/3 in the presence of a superfluid vortex. If Z3 braiding phases and angular momentum fractionalization are absent in lower density hadronic matter, as is widely expected, then the quark matter and hadronic matter regimes of dense QCD must be separated by at least one phase transition. Since the low-density regime is a confined' phase, while the high-density regime is a Higgs' phase due to color superconductivity, our results also have interesting implications for Higgs-confinement complementarity.

Thursday, October 25, 2018

12:30 pm in 464 Loomis,Thursday, October 25, 2018

#### A hierarchy of symplectic \sigma--models

Abstract: In this talk I will discuss a family of classical field theories in the Batalin--Vilkovisky formalism. These theories take as input n-symplectic Lie algebroids which correspond to symplectic manifolds, Poisson manifolds, and (higher) Courant algebroids. I will also discuss possible boundary conditions for these theories, e.g., Dirac structures and multiplectic structures. Finally, I will discuss aspects of the quantum theory in low dimensions.

Thursday, November 1, 2018

12:30 pm in 464 Loomis,Thursday, November 1, 2018

#### To Be Announced

###### Wati Taylor (MIT)

Thursday, November 8, 2018

12:30 pm in 464 Loomis,Thursday, November 8, 2018

#### Holomorphic SCFTs of small index

###### Theo Johnson-Freyd (Perimeter)

Abstract: Stolz and Teichner have conjectured that the moduli space of D=1+1, N=(0,1) QFTs provides a geometric model for Topological Modular Forms. Some important building blocks in this moduli space are the holomorphic superconformal field theories, and the conjecture leads to predictions about the possible values the supersymmetric index of such SCFTs can take. Specifically, the conjecture leads one to predict the existence of SCFTs of small nonzero index, and that the minimal possible index depends in an interesting way on the central charge of the SCFT. I will explain a construction of some SCFTs of indexes equal to the predicted minimal values. The construction leads to a new divisibility result in the seemingly unrelated field of algebraic coding theory. Based on joint work with Davide Gaiotto and Noam D Elkies.

Thursday, November 15, 2018

12:30 pm in 464 Loomis,Thursday, November 15, 2018

#### To Be Announced

###### Lampros Lamprou (MIT)

Thursday, November 29, 2018

12:30 pm in 464 Loomis,Thursday, November 29, 2018

#### To Be Announced

###### Netta Engelhardt (Princeton University)

Friday, November 30, 2018

3:00 pm in Altgeld Hall 145,Friday, November 30, 2018

#### Infinitesimals in Analysis, Topology, and Probability

###### Peter Loeb (Illinois Math)

Abstract: The notion of an infinitesimal quantity eluded rigorous treatment until the work of Abraham Robinson in 1960. Recent extensions and applications of his theory, called nonstandard analysis, have produced new results in many areas including operator theory, stochastic processes, mathematical economics and mathematical physics. Infinitely small and infinitely large quantities can play an essential role in the creative process. At the level of calculus, the integral can now be correctly defined as the nearest ordinary number to a sum of infinitesimal quantities. In Probability theory, Brownian motion can now be rigorously parameterized by a random walk with infinitesimal increments. In economics, an ideal economy can be formed from an infinite number of agents, each having an infinitesimal influence on the economy. After an introduction to this powerful method, I will discuss applications to calculus, the imbedding of topological spaces into compact spaces, and measure and probability theory. This includes the work of Y. Sun who showed that the measure spaces introduced by the present speaker can be used to finally make sense of the notion of an infinite number of equally weighted, independent random variables in probability theory and economics.

Thursday, December 6, 2018

12:30 pm in 464 Loomis,Thursday, December 6, 2018