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Events happening on October 22, 2024

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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 X Over the past two weeks we have followed the development of algebraic K-theory as a tool in homotopy theory, from Quillen's original definition for ordinary rings to the modern perspective in terms of infinity-categories. In this talk we will survey a number of tools that have been developed to compute algebraic K-theory, in particular topological Hochschild homology and topological cyclic homology in the case of ring spectra. Along the way, we will aim to connect each of these tools to the recent computations of K(Z/p^n) by Antieau-Krause-Nikolaus. Computations in Algebraic K-Theory

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