Department of

Mathematics


Seminar Calendar
for Mathematical Physics events the year of Thursday, December 7, 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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Wednesday, April 5, 2017

3:00 pm in 243 Altgeld Hall,Wednesday, April 5, 2017

Vertex algebras, chiral algebras, and factorization algebras

Emily Cliff (UIUC)

Abstract: The definition of a vertex algebra was formulated by Borcherds in the 1980s to solve algebraic problems, but these objects turn out to have important applications in mathematical physics, especially related to models of 2d conformal field theory. In the 1990s, Beilinson and Drinfeld gave geometric formulations of the definition, which they called chiral algebras and factorization algebras. These different approaches each have advantages and disadvantages: for example, the definition of a vertex algebra is more concrete and has so far been better studied; on the other hand, the geometric approach of chiral algebras and factorization algebras allows for transfer of knowledge between the fields of geometry, physics, and representation theory, and furthermore admits natural generalizations to higher dimensions. In this talk we will introduce all three of these objects; then we will discuss the relationships between them, especially focusing on how information from any one approach can lead to new understanding in the others.

Thursday, September 21, 2017

12:30 pm in 276 Loomis,Thursday, September 21, 2017

Soft particles in Effective Field Theories

Henriette Elvang (University of Michigan)

Abstract: I will discuss the approach to study quantum field theories using the soft limits of massless particles. In particular, I will present modifications to classic soft theorems for photons and gravitons that arise from higher-dimension operators in effective field theories; these can be interpreted as the corrections from loops of massive particles. Finally I will discuss on-going work on using soft limits to examine the landscape of effective field theories with enhanced symmetry.

Thursday, September 28, 2017

12:30 pm in 222 Loomis,Thursday, September 28, 2017

Conformal field theories and three point functions

Subham Dutta Chowdhury (Indian Institute of Science, Bangalore)

Abstract: Conformal invariance allows additional unique parity-odd tensor-structures for three-point functions involving the stress tensor, T, and a conserved U(1) current, j, in 2+1 dimensional conformal field theories that violate parity, apart from the usual parity even structures. Following the conformal collider physics setup of Hofman and Maldacena, we put constraints on the parity violating as well as parity preserving parameters of a general CFT in d=3. We find that large N Chern-Simons theories coupled to a fundamental fermion/boson saturate the bounds that we have derived. An application of the conformal collider bounds is observed in the form of sum rules which puts constraints on spectral densities of any CFT at finite temperature. We derive spectral sum rules in the shear channel for conformal field theories at finite temperature in general $d\geq 3$ dimensions. We show that the sum rule can be written in terms the parity even Hofman-Maldacena variables $t_2$, $t_4$ which determine the three point function of the stress tensor. We then use collider constraints and obtain bounds on the sum rule which are valid in any CFT.

Thursday, October 5, 2017

12:30 pm in 222 Loomis,Thursday, October 5, 2017

To Be Announced

Masahiro Nozaki (University of Chicago)

Thursday, October 12, 2017

12:30 pm in 222 Loomis,Thursday, October 12, 2017

Moonshine in Spacetime: Automorphy, Algebras, and String Compactifications

Natalie Paquette (Caltech)

Abstract: New examples of moonshine--- relationships between finite groups and special classes of (mock) modular forms--- have been proliferating in recent years, starting with the discovery of a Mathieu group moonshine apparently connected to conformal field theory (CFT) on the K3 surface. While many aspects of these new moonshines remain mysterious, in this talk we will stress the power of spacetime string theory---as opposed to worldsheet string theory or CFT---to shine light on some of moonshine's mysteries. We will exhibit this in two vignettes. In part 1, we give a conceptual, physical explanation of the genus zero property of Monstrous moonshine using properties of a heterotic string compactification, concomitantly placing algebraic aspects of Borcherds' proof, such as the Monstrous Lie algebra, in a physical context. This gives a precise instantiation of the role of Generalized Kac-Moody algebras organizing BPS states in string theory, as first suggested by Harvey and Moore. In part 2, we completely determine a class of elliptic genera encoding the possible symmetries acting on BPS states in K3 CFT using wall-crossing properties of spacetime BPS states on K3 x T2 and orbifolds thereof. These in turn produce a class of 1/4-BPS counting functions in spacetime. The latter are Siegel automorphic forms that constitute predictions for the reduced Gromov-Witten theory of orbifolds of K3 x T2 and account for the entropy of supersymmetric black holes.

Thursday, October 19, 2017

12:30 pm in 222 Loomis,Thursday, October 19, 2017

Soft Black Hole Absorption Rates from Large Gauge Symmetry

Steven Avery (Michigan State)

Abstract: Recently, a number of exciting connections have been made between large gauge transformations (eg. BMS) and infrared physics (eg. Weinberg's soft graviton theorem). One of the more exciting explorations in this vein was Hawking-Perry-Strominger's (HPS) investigation of the consequences of these new symmetries for black hole physics. I will show very concretely that the Ward identity for the BMS-like large U(1) gauge transformations discussed by HPS fixes the low energy black hole absorption rate for photons. Time permitting, I will discuss broader implications and future extensions.​

3:00 pm in 345 Altgeld Hall,Thursday, October 19, 2017

Hall algebras and the Fukaya category

Peter Samuleson (University of Edinburgh)

Abstract: The Hall algebra is an invariant of an abelian (or triangulated) category C whose multiplication comes from "counting extensions in C." Recently, Burban and Schiffmann defined the "elliptic Hall algebra" using coherent sheaves over an elliptic curve, and this algebra has found applications in knot theory, mathematical physics, combinatorics, and more. In this talk we discuss some background and then give a conjectural description of the Hall algebra of the Fukaya category of a topological surface. This is partially motivated by an isomorphism between the elliptic Hall algebra and the skein algebra of the torus, which we also discuss. (Joint works with H. Morton and with B. Cooper.)

Tuesday, October 24, 2017

12:30 pm in 222 Loomis,Tuesday, October 24, 2017

Entropic A theorem and the Markov property of the vacuum

Eduardo Teste (Centro Atomico de Bariloche, Argentina)

Abstract: A state is said to be Markovian if it fulfil the important condition of saturating the Strong Subadditivity inequality. I will show how the vacuum state of any relativistic QFT is a Markov state when reduced to certain geometric regions of spacetime. For the CFT vacuum, the Markov property is the key ingredient to prove the A theorem (irreversibility of the RG flow in relativistic QFT in d=4 spacetime dimensions) using vacuum entanglement entropy. This extends the entropic proofs of the c and F theorems in dimensions d=2 and d=3, giving a unified picture. I will also comment on the relation of this Markov property with the unitarity bound and holography.

Thursday, October 26, 2017

4:00 pm in 245 Altgeld Hall,Thursday, October 26, 2017

Planar graphs and Legendrian surfaces

Emmy Murphy (Northwestern)

Abstract: Associated to a planar cubic graph, there is a closed surface in R^5, as defined by Treumann and Zaslow. R^5 has a canonical geometry, called a contact structure, which is compatible with the surface. The data of how this surface interacts with the geometry recovers interesting data about the graph, notably its chromatic polynomial. This also connects with pseudo-holomorphic curve counts which have boundary on the surface, and by looking at the resulting differential graded algebra coming from symplectic field theory, we obtain new definitions of n-colorings which are strongly non-linear as compared to other known definitions. There are also relationships with SL_2 gauge theory, mathematical physics, symplectic flexibility, and holomorphic contact geometry. During the talk we'll explain the basic ideas behind the various fields above, and why these various concepts connect.

Thursday, November 2, 2017

12:30 pm in 222 Loomis,Thursday, November 2, 2017

To Be Announced

Ronak Soni (TIFR, Mumbai)

Thursday, November 9, 2017

12:30 pm in 222 Loomis,Thursday, November 9, 2017

Interface contributions to topological entanglement in abelian Chern-Simons theory

Jackson Fliss (University of Illinois at Urbana Champaign)

Abstract: Abstract: In this talk I will discuss the entanglement entropy between two (possibly) distinct topological phases in Abelian Chern-Simons theory. At the interface between the phases, two issues must be addressed: (i) what are the boundary conditions that correspond to the interface being gapped?, and (ii) how does one define entanglement in continuum gauge theories where the Hilbert space typically does not admit a tensor product factorization? For the former question it is known that gapped interfaces are described by a class of boundary conditions known as topological boundary conditions (TBCs). I will describe how TBCs also address the latter question by isolating a unique gauge invariant state in the extended Hilbert space approach. I will show that upon computing the entanglement entropy, the universal correction to the area law retains a dependence on the choice of TBCs. This result matches previous microscopic calculations found in the condensed matter literature. Additionally, when the phases across the interface are taken to be identical, this construction provides a novel explanation of the equivalence between the left-right entanglement of (1+1)d Ishibashi states and the spatial entanglement of (2+1)d topological phases.

Thursday, November 16, 2017

12:30 pm in 222 Loomis,Thursday, November 16, 2017

Quantum gravity and quantum chaos

Stephen Shenker (Stanford)

Abstract: One hallmark of chaos is sensitive dependence to initial conditions, the “butterfly effect.” We will discuss recent advances in our understanding of the quantum butterfly effect and its connection to the quantum physics of black holes. We will discuss a universal bound on the rate of development of quantum chaos motivated by these developments. Then we will briefly describe recent work on a connection between the late time behavior of black holes and the dynamics of random matrices.

Thursday, November 30, 2017

12:30 pm in 222 Loomis,Thursday, November 30, 2017

Eigenstate Thermalization and Locality and Random Matrices

Anatoly Dymarsky (University of Kentucky)

Abstract: Eigenstate Thermalization Hypothesis (ETH) is a set of properties which explain the emergence of equilibrium statistical mechanics for an isolated quantum chaotic system. It is believed to be a characteristic feature, and even used as a working definition, of quantum chaos. At the technical level ETH can be understood as an ansatz for the matrix elements of certain observables. We start by showing how ETH can help define a novel order parameter which would distinguish chaotic and non-chaotic phases. We then proceed by constraining the ETH ansatz in case of the systems with local interactions. For the systems exhibiting diffusive transport we find a new stringent bound limiting applicability of Random Matrix Theory to describe the observables satisfying the ETH.

Thursday, December 7, 2017

12:30 pm in 222 Loomis,Thursday, December 7, 2017

Conformal Truncation: A New Method for Strongly-Coupled QFTs

Zuhair Khandker (University of Illinois at Urbana Champaign)

Abstract: I will present a new numerical method for studying strongly-coupled QFTs in any dimension. The method harnesses conformal symmetry, but in a manner applicable to general, non-conformal QFTs. The input is information about the UV CFT from which the QFT originates. The output is the physical QFT spectrum, along with real-time, infinite-volume correlation functions. So far, we have used the method to study 2D phi^4 theory. I will present new results for correlation functions at any coupling, including the Zamolodchikov c-function along the full RG-flow. I will also present a non-trivial cross-check of our numerical results: for a critical value of the coupling, phi^4 theory flows to the Ising model, and we match known analytical predictions.