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Events for the weeks of April 5th – 17th

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Sun (Apr 05)	Mon (Apr 06)	Tue (Apr 07)	Wed (Apr 08)	Thu (Apr 09)	Fri (Apr 10)	Sat (Apr 11)
		Number Theory 11am @ MATH 350 Yu Fu (CalTech) X A central theme in modern arithmetic geometry is to understand the distribution of special subvarieties—loci where objects acquire extra symmetry, smaller Mumford–Tate group, or atypical monodromy. Their behavior is closely tied to conjectures on unlikely intersections, and a recurring phenomenon is that these special loci, while highly structured, are notably sparse. A natural question is how one should measure this sparsity in different arithmetic contexts. In this talk, I will discuss two illustrations of this theme. The first concerns one-parameter families of abelian varieties over number fields. How often does a specialization acquire extra endomorphisms? I will explain a quantitative result showing that such “non-generic” fibers occur on a height-density zero set of rational points. The second illustration arises from the p-adic geometry of Shimura varieties. While the Hecke orbit conjecture asserts that the prime-to-p Hecke orbit of a point is Zariski dense in the central leaf containing it, one may ask how large such an orbit can be in the p-adic analytic topology. I will describe a conjectural picture—supported by new results on p-adic monodromy—suggesting that even the full Hecke orbit is p-adically nowhere dense. Sparsity Phenomena in Arithmetic Geometry Algebra/Logic 1:25pm @ MATH 220 Nick Jamesson (CU Boulder) X The family of promise constraint satisfaction problems (PCSPs) is a variant of the well studied family of constraint satisfaction problems (CSPs). The computational problem of solving promise systems of equations over algebras is a variant of the problem of systems of equations over algebras. Given two algebras A and B of the same signature such that A maps homomorphically into B, one can ask if a system of equations has a solution in A or if it doesn't even have a solution in B. Given a finite algebra A, it is known that determining whether or not systems of equations over A have a solution is either solvable in polynomial time, or is NP complete (the famous dichotomy theorem for CSPs.) The question of whether or not a dichotomy holds for promise systems of equations over finite algebras is open in general. I will present some dichotomy results for promise systems of equations over various classes of algebras, including Mal'cev algebras. Promise Systems Of Equations Over Finite Algebras Lie Theory 2:30pm @ MATH 350 J. Carlos Martínez Mori (University of Colorado Denver) X We show that the number of zero dinv Fubini rankings with n competitors and at most l + 1 ties at any rank is given by the maximum number of regions of an l-dimensional cake with n-1 cuts. This is joint work with Pamela E. Harris and Alexander N. Wilson. Zero Dinv Fubini Rankings and Cake-Cutting Geometry	Math Phys 2:10pm @ MATH 350 Scott Maccarone (CU Boulder) Kato's theorem on the selfadjointness of the molecular Hamiltonian	Topology 1:30pm @ MATH 350 Jean-Paul Brasselet (CNRS) 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-Hélène 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-Hélène Schwartz as on her proof of the Poincaré-Hopf Theorem for singular varieties. That is a join work with Thuy Nguyen (UNESP, Rio Preto, Brazil) and Tadeusz Mostowski (Warsaw, Poland). Joint with Math Physics Seminar and CTQM Marie-Hélène Schwartz, a name on the Eiffel tower Math Phys 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-Hélène 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-Hélène Schwartz as on her proof of the Poincaré-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-Hélène Schwartz, a name on the Eiffel tower Sponsored by the Meyer Fund	Math Phys 9am @ JILA Auditorium 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 Math Phys 10:10am @ JILA… Hessel Posthuma (University of Amsterdam) X Joint with Topology Seminar and the CTQM TBA Sponsored by the Meyer Fund Math Phys 11:10am @ JILA… Marvin Qi (Kadanoff Center for Theoretical Physics) X Joint with Topology Seminar and the CTQM TBA Sponsored by the National Science Foundation Math Phys 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 Math Edu 12:20pm @ Math 220 Rebecah Deans X A large part of mathematical maturity is being able to communicate a solution to a problem clearly, as well as being able to justify to a reader that the proposed solution is correct. Even so, good communication is generally not emphasized in high school and undergraduate mathematics instruction, leaving assessment of student comprehension largely up to the instructor's interpretation. In this talk, I will discuss how MATH 2400 has attempted to improve student communication on free response exam questions by introducing a communication component to free response rubrics. I will also discuss how we have attempted to prepare both students and instructors for this new aspect of assessment. Improving and Assessing Student Communication in Coordinated Courses Math Phys 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 Math Phys 2:10pm @ JILA … David Jonas (CU Boulder) X Joint with Topology Seminar and the CTQM TBA Math Phys 3:35pm @ DUANE G126 Daniel Spiegel (Harvard Center of Mathematical Sciences and Applications) X Joint with Topology Seminar and the CTQM TBA Sponsored by the Meyer Fund Math Phys 4:40pm @ DUANE G126 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	Math Phys 9am @ JILA Auditorium Emil Prodan (Emil Prodan) X Joint with Topology Seminar and the CTQM TBA Math Phys 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 Math Phys 11:10am @ JILA… Nikita Sopenko (Institute for Advanced Studies) X Joint with Topology Seminar and the CTQM TBA Sponsored by the National Science Foundation Math Phys 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

Sun (Apr 12)	Mon (Apr 13)	Tue (Apr 14)	Wed (Apr 15)	Thu (Apr 16)	Fri (Apr 17)	Sat (Apr 18)
			Diversity 12:20pm @ MATH 350 Facilitators: Howy Jordan, Emily Montelius, and Maya Ornstein X The CHAT+ will start at 12:20. Lunch will be available at 12:00. If you plan to join, we ask that you RSVP by April 12 at the link below. There is also an option to indicate any dietary restrictions we should keep in mind. https://docs.google.com/forms/d/e/1FAIpQLSf_G3REEmhuvZwpPXpsZI-xF8UhZpRa8yfx--fjS-iigv31AQ/viewform?usp=sharing&ouid=102614817914920289902 Supporting Minority Students in Graduate Programs Math Phys 2:10pm @ Math350 Saksham Hassanandani (CU Boulder) The Bargmann-Segal representation and Schrödinger operators		PDE/Analysis 2:30pm @ MATH 350 Irina Holmes Fay (University of Wyoming) TBA Sponsored by the Meyer Fund

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