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Events for the weeks of October 20th – November 1st

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Fri, Oct. 25 5pm (Math 350)	Diversity Adriana Salerno (Bates College) X In this talk, I will show you a glimpse of one of the most exciting facets of research in modern number theory: arithmetic geometry. We will start with a (gentle) introduction to this area of research through some familiar examples. Then we will move on to a not so familiar example where we count solutions of equations mod p. I will end by answering two of the oldest and most mystifying questions in mathematics: how does this work fit into the bigger picture, and who cares? A circular tale: an introduction to arithmetic geometry
Tue, Oct. 22 12:10pm (MATH …	Kempner Daniel Martin (PhD '20) (Clemson) X “Lattice problems” drew significant interest from cryptographers in the late 90s. The belief was (and still is) that they offer an easy way to encrypt information that comes with a hard-to-hack guarantee. The popularity of lattice problems continued to rise in subsequent decades, and today they are the darlings of so-called post-quantum cryptography. This talk will show you what the fuss is all about. We will explore how lattice-based encryption works, what advantages it has over other systems, and how it invites the algebraic number theorist to the world of cryptography. No prior understanding of cryptography or number theory is necessary. Lattices and number theory in modern cryptography
Tue, Oct. 22 1pm (MATH 350)	Number Theory Colby Brown (UC Davis) X The Markoff graphs modulo p were proven by Chen (2024) to be connected for all but finitely many primes, and Baragar (1991) conjectured that they are connected for all primes, equivalently that every solution to the Markoff equation modulo p lifts to a solution over Z. In this talk, we provide an algorithmic realization of the process introduced by Bourgain, Gamburd, and Sarnak to test whether the Markoff graph modulo p is connected for arbitrary primes. Our algorithm runs in o(p^(1+epsilon)) time for every epsilon > 0. We demonstrate this algorithm by confirming that the Markoff graph modulo p is connected for all primes less than one million. Finally, we discuss other approaches to decomposing the Markoff graph, with possible applications to determining its spectral properties. Navigating the Markoff graph computationally
Tue, Oct. 22 1:25pm (Online)	Algebra/Logic Dylene Agda Souza de Barros (Universidade Federal de Uberlandia, Brasil) View Online:https://cuboulder.zoom.us/j/96896272260 X The notion of half-homomorphism between two groups is trivial, but it is an interesting subject when we drop the associativity law. In this talk, we will discuss some properties of half-homomorphism between two loops, paying special attention to some Bol loops and code loops. On half-homomorphisms of some types of Loops
Tue, Oct. 22 2:30pm (MATH 3…	Lie Theory UhiRinn Suh (Seoul National University) X Classical W-algebras, which are reductions of enveloping algebra of affine Lie algebras, have been studied in connection with Hamiltonian integrable equations. By quantization method of Hamiltonian reduction called BRST cohomology, one can get (quantum) W-algebras which are algebraic structures in Toda field theories. Moreover, conjecturally, W-algebras can be embedded in supersymmetric field theories by considering supersymmetric W-algebras obtained by supersymmetric analogue of BRST. In this talk, I will try to avoid technical details but explain basic ideas of the constructions of classical/quantum W-algebras and supersymmetric W-algebras. For last 10 mins, I will also introduce recent results related to supersymmetric W-algebras. Supersymmetry in W-algebras theory Sponsored by the Meyer Fund
Tue, Oct. 22 3:30pm (MATH 3…	Topology Alexander LaJeunesse Trace
Wed, Oct. 23 3:30pm (Math350)	Math Phys Ezzeddine El Sai (CU Boulder) The mass gap problem in Yang-Mills theory
Wed, Oct. 23 4:45pm (MATH 3…	Grad Student Seminar Matt Watson (CU Boulder) X A moduli space is a geometric space whose points parametrize some collection of geometric spaces. It is a classic result that we can construct a moduli space for 1-dimensional complex tori as the quotient $H/SL(2,Z)$ . We will review this construction and discuss how to repackage it in the language of cohomology. Equipped with this new way of viewing the moduli of complex tori, we will give a rough outline of how one might be able to use Hodge theory to construct a moduli space in some more general situations. To aid in your understanding, donuts will be provided. The Moduli Space of Complex Tori: or How I Learned to Stop Worrying and Love Hodge Theory
Thu, Oct. 24 11:15am (MATH …	Algebraic Geometry Jon Kim X We will finish explaining the minimal model program for surfaces and introduce minimal models of higher dimensional varieties. In particular, we will discuss how singularities can arise when contracting external rays in higher dimensions and how we should expand our category of minimal models to account for these singularities. Introduction to the Minimal Model Program IV (Final part)
Thu, Oct. 24 2pm (Online)	Rep Theory Lea Beneish (University of North Texas) View Online:https://cuboulder.zoom.us/j/97927772782 X We ascertain properties of the algebraic structures in towers of codes, lattices, and vertex operator algebras (VOAs) by studying the associated subobjects fixed by lifts of code automorphisms. In the case of sublattices fixed by subgroups of code automorphisms, we identify replicable functions that occur as quotients of the associated theta functions by suitable eta products. We show that these lattice theta quotients can produce replicable functions not associated to any individual automorphisms. Moreover, we show that the structure of the fixed subcode can induce certain replicable lattice theta quotients and we provide a general code theoretic characterization of order doubling for lifts of code automorphisms to the lattice-VOA. Finally, we prove results on the decompositions of characters of fixed subVOAs. This talk is based on joint work with Jennifer Berg, Eva Goedhart, Hussain M. Kadhem, Allechar Serrano López, and Stephanie Treneer. Replicable functions arising from code-lattice VOAs fixed by automorphisms
Thu, Oct. 24 2:30pm (Zoom)	Functional Analysis A. Sitarz (Moved to Zoom) (Jagiellonian University, Poland) View Online:https://cuboulder.zoom.us/j/92986030547 Meeting ID: 929 8603 0547 X Carla Farsi is inviting you to a scheduled Zoom meeting. Join Zoom Meeting https://cuboulder.zoom.us/j/92986030547 Meeting ID: 929 8603 0547 Starting from the classical situation and the abstract algebraic approach, we propose an operatorial definition for a connection and compatibility between the connection and the Dirac operator on the total space and on the base space of the bundle. An example of the noncommutative three-torus viewed as a U(1) bundle over the noncommutative two-torus gives all connections compatible with an admissible Dirac operator. Conversely, a family of new Dirac operators on the noncommutative tori is found, which arise from the base-space Dirac operator and a suitable connection. Based on a joint work with Ludwik Dabrowski. Noncommutative circle bundles and new Dirac operators
Mon, Oct. 28 4:45pm (MATH 3…	Grad Student Seminar Sylvia Maher (CU Boulder) X What do the trace of a matrix, the cycle type of a permutation, and the Euler characteristic of a CW complex have in common? In this talk I will investigate the key categorical properties of the trace of a matrix and show how we can generalize this idea to talk about 'traces' in other contexts. The universal property of the trace
Tue, Oct. 29 2:30pm (MATH 3…	Lie Theory Jen Gensler (CU) X TBA TBA
Tue, Oct. 29 3:30pm (MATH 3…	Topology Yang Hu (New Mexico State University) X The orthogonal/unitary calculus of Weiss is a framework of studying functors from vector spaces to topological spaces. Each such functor has an associated Taylor tower — a tower of fibrations whose layers are infinite loop spaces. When applied to the functor BO(-) or BU(-), Weiss calculus provides a "custom-made" resolution for the classifying spaces, allowing for the program of enumerating unstable vector bundles with stable calculations. In this talk, we present old and new enumeration results along this program and discuss, if time allows, an equivariant version of the story. This talk contains joint work with Hood Chatham and Morgan Opie, and work in progress with Prasit Bhattacharya. Bundle-counting with calculus
Thu, Oct. 31 11:15am (MATH …	Algebraic Geometry Sebastian Casalania-Martin TBA
Thu, Oct. 31 2pm (Online)	Rep Theory Justine Fasquel (University of Melbourne) View Online:https://cuboulder.zoom.us/j/97927772782 TBA
Fri, Nov. 1 2:30pm (MATH 2…	Grad Algebra/Logic Nick Jamesson X We discuss properties of commutators for algebras in congruence modular varieties. The commutator in congruence modular varieties

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