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Events happening on October 14, 2025

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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

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