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Events for February – June

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Thu, Mar. 13 5pm	Functional Analysis Jordan Watts (University of Central Michigan) TBA
Tue, Feb. 4 1:25pm (MATH 2…	Algebra/Logic Peter Mayr (CU) View Online:https://cuboulder.zoom.us/j/96896272260 X Commutators have been generalized from groups to arbitrary algebras in different ways. I will give an overview of the properties of the binary term condition commutator and higher commutators from universal algebra specialized to semigroups and the derived notions of nilpotence, supernilpotence, and solvability. Finite supernilpotent semigroups
Tue, Feb. 4 2:30pm (MATH 2…	Grad Algebra/Logic Keith Kearnes (CU) View Online:https://cuboulder.zoom.us/j/96896272260 The structure of finite algebras, 2
Tue, Feb. 4 2:30pm (MATH 3…	Lie Theory Nat Thiem (CU) X This talk is a largely expository how-to guide for building a representation theory that categorifies your favorite combinatorial Hopf algebra. The goal is to present a general framework that captures both the classical examples (symmetric group, general linear groups) and more modern examples (upper-triangular groups and tori) with an eye towards new families of examples. Turning the representation theory of matrix groups into combinatorial Hopf algebras
Tue, Feb. 4 3:30pm (MATH 3…	Topology Ezzeddine El Sai (CU Boulder) X It is very well known that homological algebra can be very ill behaved when enriched over topological spaces. This begs the question, how should one study geometry over topological fields? One radical idea by Clausen and Scholze is to do away with topology all together and start from scratch in what they call "Condensed Mathematics". In this talk we will discuss the merits of this approach and pose the question "what actually is a space?" Geometry without Topology
Wed, Feb. 5 3:30pm (MATH350)	Math Phys Gregory Berkolaiko (Texas A&M University) X Occurence of multiple eigenvalues in families of self-adjoint operators is a question with numerous applications in mathematical physics. In this expository talk we will review the "no accidental multiplicities in one parameter" result of Wigner and von Neumann, the "typical" conical shape of eigenvalue multiplicities in two parameters, and the use of geometric phase (often called the "Berry phase" but in this case used earlier by Herzberg and Longuet-Higgins) to understand why the conical intersections cannot be destroyed without leaving the class of real operators. Theory will be illustrated by numerical simulations and the content will be kept accessible to advanced undergraduate students. Geometric Phase and Stability of Conical Intersections
Thu, Feb. 6 11:15am (MATH …	Algebraic Geometry Matt Watson X D-Modules are algebraic objects which can be used in the study of linear PDEs on a complex algebraic variety. In this talk we will give a definition and see how D-modules correspond to flat connections. If time allows we may cover left and right D-modules, coherence, or good filtrations. Introduction to D-Modules
Thu, Feb. 6 2:30pm (MATH 3…	Functional Analysis James Woodcock (CU Boulder) The Dirac-dual Dirac method
Mon, Feb. 10 3:35pm (MATH 3…	Grad Student Seminar Alex LaJeunesse (CU Boulder) X We'll discuss what it means to (repeatedly) categorify abelian groups and how this is related to higher notions of additivity in infinity-categories, as well as recent developments in chromatic homotopy theory. Delooping Primes
Tue, Feb. 11 2:30pm (MATH 3…	Lie Theory Jinwei Yang (Shanghai Jiao Tong University) X In a series of celebrated work, D. Kazhdan and G. Lusztig constructed braided tensor category structure on the category of finite length modules for the affine Lie algebras when the level plus dual Coxeter number is not a positive rational number, and proved that the category is equivalent to the category of finite dimensional weight modules for the quantum groups. In this talk, we discuss our recent progress on tensor categories at positive rational levels using vertex operator algebra approach. Concretely, We construct braided tensor category structure on the category of ordinary modules for simple affine vertex operator algebras and prove rigidity in some cases. For affine sl_2 Lie algebra, we also study two bigger representation categories, one is the category of weight modules for the simple affine vertex operator algebra, which is neither finite or semisimple, we prove its rigidity, the other is the category of finite length modules for the universal affine vertex operator algebra, we show this category is derived equivalent to the category of the quantum groups. This talk is based on a series of joint work with T. Creutzig, Y.-Z. Huang and R. McRae. Representation and tensor category of affine sl_2 Lie algebra at positive rational level Sponsored by the Meyer Fund
Tue, Feb. 11 3:30pm (MATH 3…	Topology James Woodcock TBD
Wed, Feb. 12 3:30pm (MATH350)	Math Phys Sheagan John (CU Boulder) X TBA Foundations of Measure Theory
Thu, Feb. 13 11:15am (MATH …	Algebraic Geometry Daniel Lyness TBA
Fri, Feb. 14 11:15am (Math …	Math Edu Rebecca Machen X This workshop will introduce mathematics educators to the transformative potential of generative AI tools, such as ChatGPT, for fostering dynamic, student-centered learning experiences. We will focus on a customized GPT model designed for students to use this semester, which emphasizes problem-solving, self-reflection, and personalized feedback on mathematical concepts. By the end of the session, participants will gain practical strategies for leveraging generative AI to create engaging and supportive learning environments that encourage students to take active ownership of their education. No prior AI experience needed and plan to bring a laptop for use. Enhancing Mathematical Problem-Solving Skills and Academic Mindsets for Undergraduate Mathematics Students Through Interactions with Generative AI
Mon, Feb. 17 3:30pm (Kitt C…	DeLong Laura DeMarco (Harvard University) X The field of dynamical systems has a long and fascinating history: it originated with the study of planetary motion and has become a central part of mathematics today. In this talk, I will present some of its historical development, with emphasis on the subtle question of linearization and how that leads to deep and difficult problems that remain unsolved. From the solar system to the Mandelbrot set Sponsored by the Meyer Fund
Tue, Feb. 18 12pm (MATH 350)	Algebraic Geometry Mihnea Popa (Harvard) X TBD TBD Sponsored by the Meyer Fund
Tue, Feb. 18 1:25pm (MATH 2…	Algebra/Logic Johanna Brunar (TU Wien, Austria) View Online:https://cuboulder.zoom.us/j/96896272260 X Conservative graph-colouring problems, also known as list homomorphism problems, have been examined for various classes of finite digraphs. Each instance consists of a finite digraph along with a list of permitted values for each vertex. Lifting the scenario to infinite digraphs G, the 1-orbits of an oligomorphic subgroup $Ω$ of Aut(G) take the role of elements. A conservative template in this framework is enriched by a unary relation for all unions of 1-orbits of $Ω$ . Assuming only access to unions of pairs of 1-orbits, we obtain the first structural dichotomy for $ω$ -categorical smooth digraphs of algebraic length 1, yielding a hardness criterion for the respective conservative graph-colouring problems. We thereby overcome previous obstacles to lifting structural results for digraphs in this context from finite to $ω$ -categorical structures -- the strongest lifting results hitherto applying only to undirected graphs. This is joint work with Marcin Kozik, Tomas Nagy, and Michael Pinsker. The sorrows of a smooth digraph
Tue, Feb. 18 3:30pm (MATH 3…	Topology Alex Lajeunesse TBD
Tue, Feb. 18 3:30pm (Kitt C…	DeLong Laura DeMarco (Harvard University) The geometry (and algebra) of the Mandelbrot set Sponsored by the Meyer Fund
Wed, Feb. 26 3:30pm (MATH350)	Math Phys Howy Jordan (CU Boulder) X TBA Foundations of Quantum Mechanics
Thu, Feb. 27 11:15am (MATH …	Algebraic Geometry Jon Kim TBA
Thu, Feb. 27 3:35pm (MATH 3…	Probability Mike Cranston (UCI) TBD
Fri, Feb. 28 11:15am (Math …	Math Edu Lee Roberson X As teachers, we use the power of questions to assess and build our students’ mathematical understanding. The questions we ask can determine how our students think about concepts, respond to inquiry, collaborate with others, connect ideas, and ask their own questions. Because of this, we will take time to pause and reflect on the questions we ask in our classes. We will question the purpose of our questions, the types of questions we ask, and the questioning strategies we use to better understand our own pedagogical practices so that we can improve our students’ mathematical understanding. Questioning Our Questions
Thu, Mar. 6 11:15am (MATH …	Algebraic Geometry Nolan Schock (UIC) X TBD TBD Sponsored by the Meyer Fund
Tue, Mar. 11 12:10pm (MATH …	Kempner Edmund Harriss (University of Arkansas) TBA
Tue, Mar. 11 1:15pm (MATH 3…	Geometry/Analysis Tristan Léger (Yale University) X In this talk I will discuss recent and upcoming results on the boundedness of spectral projectors. The seminal work of C. Sogge gives the optimal result on any Riemannian manifold with bounded geometry for spectral windows of size 1. However when the width is smaller, the spectral projector bounds become sensitive to the global geometry of the underlying manifold. I will focus on the case of hyperbolic surfaces of infinite area, and present new estimates that hold universally in that setting. This is joint work with Jean-Philippe Anker and Pierre Germain. Spectral projector bounds on hyperbolic surfaces of infinite area Sponsored by the Meyer Fund
Wed, Mar. 12 3:30pm (MATH350)	Math Phys Ezzeddine El Sai (CU Boulder) X TBA Statistics and Mathematical Physics
Thu, Mar. 13 11:15am (MATH …	Algebraic Geometry Jon Kim TBA
Tue, Mar. 18 3:30pm (MATH 3…	Topology Alex LaJeunesse (CU Boulder) TBD
Wed, Mar. 19 3:30pm (MATH350)	Math Phys Ezzeddine El Sai (CU Boulder) X TBA Statistical Learning
Thu, Mar. 20 11:15am (MATH …	Algebraic Geometry Ruijie Yang (Kansas) X TBD TBD Sponsored by the Meyer Fund
Thu, Mar. 20 2:30pm (MATH 3…	Functional Analysis Laura Scull (Fort Lewis College) TBA
Thu, Mar. 20 3:35pm (MATH 3…	Probability Giorgio Cipolloni (University of Arizona) TBA
Wed, Apr. 2 3:30pm (MATH350)	Math Phys Markus Pflaum (CU Boulder) X TBA Born-Oppenheimer Approximation
Thu, Apr. 3 11:15am (MATH …	Algebraic Geometry Patricio Gallardo (UC Riverside) X TBA TBA Sponsored by the Meyer Fund
Tue, Apr. 8 3:30pm (MATH 3…	Topology Stephanie Oh (CU Boulder) TBD
Wed, Apr. 9 3:30pm (MATH350)	Math Phys Wilson Wu (CU Boulder) X TBA Neural Networks
Mon, Apr. 14 3:35pm (MATH 3…	Grad Student Seminar Chris Eblen (CU Boulder) X Schur--Weyl duality is a fundamental paradigm in representation theory relating representations of the general linear group to those of the symmetric group. We will discuss the classical case of Schur--Weyl duality and an analog for the unipotent upper triangular matrix group over a finite field. Then we will define supercharacter theory and how a particular supercharacter theory for the unipotent upper triangulars, within the context of this Schur--Weyl duality analog, lead to a class of modules called beach modules and a collection of projection-like maps in the centralizer algebra. A Day at the Beach
Wed, Apr. 16 3:30pm (MATH350)	Math Phys TBD X TBA Hartree-Fock Method
Wed, Apr. 23 3:30pm (MATH350)	Math Phys TBD X TBA Mathematical Foundations of Deep Learning
Fri, Apr. 25 2:30pm (MATH 3…	Geometry/Analysis Maja Taskovic (Emory University) TBA Sponsored by the Meyer Fund
Tue, Apr. 29 3:30pm (MATH 3…	Topology Emily Montelius (CU Boulder) TBD
Wed, Apr. 30 3:30pm (MATH350)	Math Phys TBD X TBA Schrodinger Operator in Quantum Chemistry

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