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Events for Mathematical Physics

ICS calendar file for Math Phys

This file can be used to add scheduled events to your calendar, however every program is unique. Below you will find what information is available, but if nothing else works try creating a new calendar in your program and using

http://math.colorado.edu/seminars/ics/mphy.ics

as the source.

Thunderbird

The Mathematical Physics Seminar will explore various topics under the umbrella of Poisson geometry, quantum mechanics, and the geometry of classical and quantum fields. This seminar is organized by Markus Pflaum and Gregory Berkolaiko.

Wed, Apr. 1 2pm (MATH350)	Evan Wickenden (CU Boulder Physics) Periodic Schr�dinger operators and Bloch theory II
Thu, Apr. 2 2:10pm (MATH220)	Jorgen Ellegaard Andersen (University of Southern Denmark) X We will consider Geometric Quantization on general K�hler phase spaces and propose a program for compatible constructions of the quantization of functions, the Hilbert space structure, and the dependence on the choice of the K�hler structure (generalized Hitchin connection), fixing only the underlying symplectic manifold and a prequantum line bundle. We will in particular see explicitly how the curvature of the phase space modifies the quantization. Geometric Quantization of General K�hler Manifolds
Wed, Apr. 8 2:10pm (MATH 3…	Scott Maccarone (CU Boulder) Kato's theorem on the selfadjointness of the molecular Hamiltonian
Thu, Apr. 9 1:30pm (Math350)	Jean-Paul Brasselet (CNRS, Marseille) X When he built his tower, Gustave Eiffel engraved the names of 72 French scientists, all men. Recently, it has been decided to engrave the names of 72 French women scientists on the tower. Eleven mathematicians were selected, including Marie-H�l�ne Schwartz. One of her major works, in 1965, was the construction of characteristic classes for singular complex analytic varieties. This result was subsequently part of a conjecture by Grothendieck and Deligne, proved by Robert MacPherson. The classes are now called "Schwartz-MacPherson classes. The elementary presentation will focus as much on the life of Marie-H�l�ne Schwartz as on her proof of the Poincar�-Hopf Theorem for singular varieties. That is a join work with Thuy Nguyen (UNESP, Rio Preto, Brazil) and Tadeusz Mostowski (Warsaw, Poland). Joint with Topology Seminar and CTQM Marie-H�l�ne Schwartz, a name on the Eiffel tower Sponsored by the Meyer Fund
Fri, Apr. 10 9am (JILA Audi…	Martin Schottenloher (TU Munich) X Link to PDF abstract https://drive.google.com/file/d/1g3eW-mgXx6HA4sX61rQcrIaVFK7L0Xc1/view Joint with Topology Seminar and the CTQM Geometric Quantization: A mathematical path to quantum models Sponsored by the Meyer Fund
Fri, Apr. 10 10:10am (JILA …	Hessel Posthuma (University of Amsterdam) X I�ll start by giving an introduction to index theory in the presence of symmetries and explain how this fits into the framework of noncommutative geometry. After that I will focus on the case of proper actions of groups and explain a recent "higher fixed point formula" obtained in joint work with Paolo Piazza, Yanli Song and Xiang Tang. Joint with Topology Seminar and the CTQM Higher index theory for proper actions Sponsored by the Meyer Fund
Fri, Apr. 10 11:10am (JILA …	Marvin Qi (Kadanoff Center for Theoretical Physics) X Symmetries and anomalies provide powerful constraints on the dynamics of quantum many-body systems. In this talk, I will revisit a class of models known as quantum dimer models, and argue for the presence of a mixed anomaly involving lattice rotations and a higher-form symmetry. This anomaly forbids the existence of any symmetry preserving gapped phase, consistent with the known phase diagrams of these models. This talk is based on work in progress with Wilbur Shirley and Clay C�rdova. Joint with Topology Seminar and the CTQM Lattice anomalies in quantum dimer models Sponsored by the National Science Foundation
Fri, Apr. 10 11:40am (JILA …	Laura Shou (University of Maryland) X Joint with Topology Seminar and the CTQM Exactly solvable topological phase transition in a quantum dimer model Sponsored by the National Science Foundation
Fri, Apr. 10 12:30pm (JILA …	Anton Kapustin (California Institute of Technology) X It is expected that a generic closed many-body system prepared in a well-behaved initial state will eventually thermalize, i.e. approach a Gibbs state. This property, while compatible with and even demanded by the physical intuition, is much stronger than ergodicity or mixing and is difficult to justify mathematically. Similarly, a generic many-body system subject to a periodic drive (a Floquet system) is expected to heat up and approach the state of maximal entropy. In this talk I will describe an infinite set of many-body Floquet systems of algebraic origin, both classical and quantum, for which thermalization of very general initial states can be studied analytically as well as numerically. Joint with Topology Seminar and the CTQM Thermalization and chaos in many-body quantum and classical dynamical systems of algebraic origin
Fri, Apr. 10 2:10pm (JILA …	David Jonas (CU Boulder) X The Born-Oppenheimer or adiabatic approximation separates fast electronic dynamics from slow nuclear dynamics. In this approximation, the electronic Schr�dinger equation is solved for fixed nuclei and then each electronic energy is used as a potential energy surface for solving the vibrational Schr�dinger equation. Von Neuman and Wigner put forth a dimensional argument that the potential curves should avoid each other in diatomic molecules but that potential surfaces should have intersections in polyatomic molecules. With the local shape of a double-cone in 2D, these conical intersections have been identified by their associated topological phase (Berry phase) and are now known to occur in many photochemical reactions. Nevertheless, they are features of an approximation. Several years ago, we were exploring a non-adiabatic model for energy transfer in photosynthesis and found that the exact non-adiabatic eigenfunctions have a weird nodal structure that parallels the dimensional arguments of Von Neuman and Wigner. Instead of the usual nodal points in 1D, nodal curves in 2D, etc. the nonadiabatic eigenfunctions have avoided nodes in 1D, point nodes in 2D, etc. In the neighborhood of a point node in 2D, the nonadiabatic eigenfunctions have the local shape of a cone. High symmetry can generate higher order nodes. The nodes have a signed integer electronic index that measures electronic state vector rotation around a closed vibrational path and is locally stable to perturbations. I will discuss examples of conical nodes that occur by accident and near symmetry-required conical intersections. M. Born, Gott. Nachr. math. phys. Kl. 6, 1 (1951). J. von Neumann and E. Wigner, Phys. Z. 30, 467 (1929). M. V. Berry, Proc. R. Soc. Lond. A 392, 45 (1984). M. Klessinger and J. Michl, Excited States and Photochemistry of Organic Molecules. (VCH Publishers, New York, 1995). V. Tiwari, W. K. Peters and D. M. Jonas, Proc. Natl. Acad. Sci. USA 110, 1203 (2013). P. W. Foster, W. K. Peters and D. M. Jonas, Chem. Phys. Lett. 683, 268 (2017). P. W. Foster and D. M. Jonas, J. Phys. Chem. A 121, 7401 (2017); 123, 1273 (2019). P. W. Foster and D. M. Jonas, Chem. Phys. 520, 108 (2019). Joint with Topology Seminar and the CTQM The weird geometry of non-adiabatic eigenfunctions
Fri, Apr. 10 3:35pm (DUANE …	Daniel Spiegel (Harvard Center of Mathematical Sciences and Applications) X Matrix product states form an especially tractable and well-understood class of states of quantum spin chains. In particular, when working with matrix product states, one obtains elegant derivations of various topological indices that classify phases of both symmetry protected states as well as continuously parametrized families of states. I will begin this talk with a brief introduction to matrix product states on infinite lattices, move on to discuss joint work with my CU Boulder colleagues on the homotopy type of the space of matrix product states, and finally I will mention work in progress on the classification of matrix product states that are both symmetry-protected and parametrized. Joint with Topology Seminar and the CTQM Parametrized Families of Matrix Product States Sponsored by the Meyer Fund
Fri, Apr. 10 4:40pm (DUANE …	Xiang Tang (Washington St Louis) X Let G be a connected linear real reductive group with a maximal compact subgroup K. In this talk, we will discuss an approach to studying the large-time behavior of the heat kernel on the corresponding homogeneous space G/K using Bismut's formula. We will try to explain how Bismut's formula provides a natural link between the index theory and representation theory. In particular, Vogan's lambda-map in the representation theory of G plays a central role in the large time asymptotic analysis about the trace of the heat kernel. This talk is based on joint works with Shu Shen and Yanli Song. Joint with Topology Seminar and the CTQM The large time behavior of the heat kernel on homogenous spaces and Bismut's formula Sponsored by the Meyer Fund
Sat, Apr. 11 9am (JILA Aud…	Emil Prodan (Emil Prodan) X I will describe how to deal with single-particle dynamics over complex aperiodic discrete geometries using C-algebras. Using numerical examples, I will first convey that any local Hamiltonian over such a geometry falls into one and same algebra, completely determined by the underlying discrete geometry. I will then describe this algebra based on the notion of phason spaces, and compute it for particular cases (e.g. twisted bilayers). K-theory of this algebra tells us what topological invariants are available for a given discrete geometric structure. For example, a twisted bilayer can host up to second-Chern numbers but nothing above that. The punch line of the talk would be a C-formulation of ordinary and higher order bulk-defect correspondences. The claim is that, given a geometry with defects (surfaces, hinges, corners, dislocations, disclinations, etc), the C-algebraic framework supplies a device to enumerate all possible non-trivial defect-boundary correspondences, without missing one. I will include numerical demonstrations of these principles. References: P. D. Ojito, E. Prodan, T. Stoiber, C-framework for higher-order bulk-boundary correspondences, Comm. Math. Phys 406, 233 (2025). B. Mesland, E. Prodan, Classifying the dynamics of architected materials by groupoid methods, Journal of Geometry and Physics 196, 105059 (2024). Joint with Topology Seminar and the CTQM Taming Spatial Complexity in Topological Dynamics with C*-Algebras
Sat, Apr. 11 10:10am (JILA …	Henri Moscovici (Ohio State University) X My talk centers on an �ordinary-looking� ordinary differential equation�the prolate spheroidal wave operator�which has played a surprisingly rich and unexpected role across several fields. It first arose as a �lucky accident� in the 1960s solution by Slepian, Landau, and Pollak of the problem of time-and band-limiting of signals, raised by Claude Shannon. The same operator reappeared in the late 1990s through a cutoff mechanism in Alain Connes� trace formula reformulation of the Weil explicit formula in number theory. More recently, in joint work with Connes (2022), we found that when this operator is extended from a finite interval to the whole line, its spectrum reproduces�with striking accuracy�the squares of the imaginary parts of the zeros of the Riemann zeta function. I will conclude with a refinement of this phenomenon based on analyzing the operator in the complex domain. Joint with Topology Seminar and the CTQM The unlikely bond between the prolate wave operator and Riemann�s zeta function Sponsored by the Meyer Fund
Sat, Apr. 11 11:10am (JILA …	Nikita Sopenko (Institute for Advanced Studies) X Gapped phases of two-dimensional free-fermionic systems without any symmetry are classified by an integer-valued topological invariant called the Chern number, which counts the net chirality of boundary modes. It has long been conjectured that systems with distinct Chern numbers cannot be deformed into each other without a phase transition, even in the presence of arbitrarily strong interactions. In this talk, I will present a construction of a many-body index that generalizes the Chern number to the interacting setting and allows us to prove this conjecture. When the edge modes can be described by a conformal field theory, the index provides a microscopic characterization of the chiral central charge. Joint with Topology Seminar and the CTQM A many-body index for 2d topological superconductors Sponsored by the National Science Foundation
Sat, Apr. 11 11:40am (JILA …	Michael Hermele (CU Boulder) X There are now many examples of gapped fracton models, which are defined by the presence of restricted-mobility excitations above the quantum ground state. This complex landscape of examples is far from being mapped out. In this talk, I will describe recent progress on characterization and classification of fracton orders, and on related problems for subsystem symmetries. Joint with Topology Seminar and the CTQM Navigating the Fracton Landscape
Wed, Apr. 15 2:10pm (Math350)	Saksham Hassanandani (CU Boulder) The Bargmann-Segal representation and Schr�dinger operators
Wed, Apr. 22 2:10pm (Math350)	Mudassir Moosa (CU Boulder Physics) X The AdS/CFT correspondence establishes a duality between a gravitational theory in an Anti-de Sitter (AdS) spacetime and a conformal quantum field theory on the boundary of the spacetime. This has led to the notion that the spacetime is an emergent concept, but how it emerges from quantum theory on a boundary is not fully understood. In this talk, I will discuss some work in this direction using the theory of von Neumann algebras. Specifically, I will consider a (non-local) conformal Generalized Free Field theory dual to a local scalar field theory in AdS_2 spacetime and will explore the properties of the modular flow and modular conjugation of "time-interval algebras". I will show that these algebras satisfy "Holographic Algebraic Properties". Moreover, I will prove the converse statement that the existence of Holographic Algebraic Properties in any quantum system implies a local QFT in an AdS_2 spacetime. This explains the emergence of a local spacetime in a simple setup. von Neumann Algebras in Holography and Emergence of Spacetime
Wed, Apr. 29 2:10pm (Math350)	Gregory Berkolaiko (Texas A&M) X In this pedagogical talk, we will discuss a simple setting in which to explore the methods we saw in Evan Wickenden's talk earlier this semester: discrete Schrodinger operators (1d periodic). We will compare the two methods that were introduced: the Floquet discriminant and the Bloch transform. In the 1d periodic case, there are some patterns predicted by Hill's theorem which can be disturbed by a suitably strong perturbation of the operator. The latter observation is related to some ideas of spectral engineering: resonant gap opening and flat bands. We will not present any research results, although some numerical simulation we will see may lead to a research project. Explorations of periodic Schrodinger operator

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Events for Mathematical Physics