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Events for the weeks of October 12th – 24th

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Tue, Oct. 14 12:10pm (MATH …	Kempner Constantin Dorin Dumitrascu (Adrian College) X We take a combinatorial approach to the classical problem of random walks in the d-dimensional Euclidean lattice Z^d, where the walker takes steps {-1, +1}^d, each with equal probability 1/(2d). We give precise asymptotics for the number of closed walks or excursions (the walks of a given length that return to the starting point). We also discuss the more complicated case of first-time returns. Recall that a sequence (f_n)_n is called P-recursive if it admits a recurrence relation with coefficients polynomials in n. This property is equivalent with holonomicity (or D-finiteness) of the generating function, meaning that the vector space of its formal derivatives is finite dimensional. We show that, in dimension greater or equal to 2, the sequence of excursions is P-recursive, while the sequence of first-time returns is not P-recursive. Techniques from the theory of Legendre polynomials, analytic combinatorics, holonomic functions, and Fuchsian ODEs are employed in the proofs. This presentation reports on joint work with Liviu Suciu. On the non-holonomic character of first time returns in the Euclidean lattice
Tue, Oct. 14 2:30pm (MATH 2…	Grad Algebra/Logic Nick Jamesson (CU Boulder) Categorical Perspective on Constraint Satisfaction (Part 4)
Tue, Oct. 14 2:30pm (MATH 3…	Lie Theory Richard Green (CU) X We explore further applications of the generalized Rothe diagrams associated to sets of orthogonal positive roots of simply laced root systems. We will discuss examples arising from labelled Fano planes and from the representation theory of simple Lie algebras. This talk is based on joint work with Tianyuan Xu (University of Richmond), and is a continuation of last week's talk. Orthogonal roots and generalized Rothe diagrams, part 2
Tue, Oct. 14 3:30pm (MATH 3…	Topology Taylor Rogers X Recently, higher categorical generalizations of semiadditivity have proven useful in stable homotopy theory; in particular, they demonstrate that certain localizations of the category of spectra are exceedingly well-behaved. Understanding higher semiadditivity has also produced an interesting theory of ambidextrous adjunctions, that may be useful in the study of other stable infinity categories. In this talk, we will introduce semiadditivity and ambidexterity in a general categorical setting. We will then specialize to the context of stable homotopy theory and discuss how the theory of higher semiaddtivity gives a proof of May's nilpotence conjecture. Ambidexterity and Nilpotence
Tue, Oct. 14 3:35pm (MATH 2…	PDE/Analysis Fernando Charro (Wayne State University) X In recent years there has been an increasing interest in whether a mean value property, known to characterize harmonic functions, can be extended in some weak form to solutions of nonlinear equations. This question has been partially motivated by the surprising connection between Random Tug-of-War games and the normalized p-Laplacian discovered some years ago by Peres et al., where a nonlinear asymptotic mean value property for solutions of a PDE is related to a dynamic programming principle for an appropriate game. In this talk, we discuss asymptotic mean value formulas for a class of nonlinear second-order equations that includes the classical Monge-Ampère and k-Hessian equations among other examples. Asymptotic Mean Value Formulas for Nonlinear Equations Sponsored by the Meyer Fund
Thu, Oct. 16 11:15am (MATH …	Algebraic Geometry Matt Watson X TBA TBA
Thu, Oct. 16 2:30pm (MATH 3…	Functional Analysis Gregory Berkolaiko (Texas A&M) X Duistermaat index is a symplectic invariant defined for triples of Lagrangian subspaces. We discuss its concise axiomatic definition, its relation to the Maslov index of paths of Lagrangian subspaces and its surprising application to eigenvalue interlacing for differential operators with different sets of boundary conditions. Based on joint work with Graham Cox, Yuri Latushkin and Selim Sukhtaiev. Duistermaat index and its application to eigenvalue interlacing
Tue, Oct. 21 2:30pm (MATH 3…	Lie Theory Andrew Reimer-Berg (Colorado State University) X We resolve a question of Gillespie, Griffin, and Levinson that asks for a combinatorial bijection between two classes of trivalent trees, tournament trees and slide trees, that both naturally arise in the intersection theory of the moduli space of stable genus zero curves with n marked points. In this talk, we give an explicit combinatorial bijection between these two sets of trees using an insertion algorithm, and also classify the words that appear on the slide trees of caterpillar shape via pattern avoidance conditions. Insertion algorithms and pattern avoidance on trees coming from the moduli space of curves
Tue, Oct. 21 2:30pm (MATH 2…	Grad Algebra/Logic Nick Jamesson (CU) Categorical Perspective on Constraint Satisfaction (Part 5)
Tue, Oct. 21 3:30pm (MATH 3…	Topology Alex LaJeunesse X Machinery from homotopy theory allows us to define a Brauer space for any E_3-ring R whose homotopy groups carry important arithmetic information about R. If R is equivalent to a discrete commutative ring, for example, these homotopy groups agree with the classical (derived) unit, Picard, and Brauer groups. I will describe how one constructs this Brauer space and discuss the problem of "strictification" for Brauer classes. Unit, Picard, and Brauer Groups of Ring Spectra
Wed, Oct. 22 4:40pm (MATH 3…	Grad Student Seminar Edouard Heitzmann (CU Boulder) X I will state Arrow's Impossibility Theorem, then give the definitions of some commonly used ranked-choice voting rules, and finally present some examples of common paradoxes that each of them suffer from. Some Common Voting Rule Paradoxes
Thu, Oct. 23 11:15am (MATH …	Algebraic Geometry Yota Maeda (TU Darmstadt) X See https://sites.google.com/view/fragmentseminar/ On the Kodaira dimension of even-dimensional ball quotients Sponsored by the Meyer Fund

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