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9:00am to 4:00pm - NS II 1201 - Combinatorics and Probability - (UCI) Southern California Discrete Mathematics Symposium 2025 SoCalDM is a friendly, day-long research conference designed for discrete mathematicians in Southern California. For more details please visit the conference website: https://sites.google.com/view/socaldm2025/home Here is the schedule for the event: 9:00-9:30 Welcome coffee 9:30-10:00 Jonathan Davidson (Cal State LA), A Combinatorial Design Approach to a Multicolor Bipartite Ramsey Problem 10:10-10:40 Lenny Fukshansky (Claremont McKenna College), On a new absolute version of Siegel’s lemma 10:40-11:00 Coffee Break 11:00-11:30 Mason Shurman (UCI), Covering Random Digraphs with Hamilton Cycles 11:40-12:10 Claire Levaillant (USC), Solutions to the Diophantine equation $\sum_{i=1}^n\frac{1}{x_i}=1$ in integers of the form p^a*q^b with p and q two distinct primes. 12:10-2:00 Lunch 2:00-2:30 Sehun Jeong (Claremont Graduate University), Integral quadratic forms and lattice angles 2:40-3:10 Justin Troyka (Cal State LA), Growth rates of permutations with given descent or peak set 3:20-3:50 Yizhe Zhu (USC), CLTs for linear spectral statistics of inhomogeneous random graphs |
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4:00pm to 5:00pm - RH 340P - Geometry and Topology Emil Geisler - (UCLA) Computations in Representation Stability We recall the notion of representation stability in the context of the cohomology of ordered configuration space of the plane. We give examples of the computation of stable multiplicities by arithmetic methods using the Grothendieck-Lefschetz fixed point formula and describe how these methods lead to a general algorithm and proofs of specific asymptotics. |
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4:00pm - RH 440R - Logic Set Theory Alex Berenstein - (Universidad de los Andes) Group algebras as Banach lattices We will define L_1 Banach lattices and recall some of its model theoretic properties. We will then consider group algebras associated to locally compact groups, where the multiplication is convolution and we will consider them as L_1 Banach lattices. We will show that such expansions carry deep information about the underlying group. For example, when the group is discrete, the group will be definable inside the expansion. In particular, we show, for discrete groups, that if two group algebras are elementary equivalent, then the corresponding groups are elementary equivalent. This is joint work with K. Gannon and S. Song. |
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4:00pm to 5:00pm - RH 340N - Applied and Computational Mathematics Angxiu Ni - (UC Irvine) Differentiating unstable diffusions We derive the path-kernel formula for the linear response, the parameter derivative of averaged observables, of SDEs. Here the parameter controls initial conditions, drift coefficients, and diffusion coefficients. Our formula tempers the unstableness by gradually moving the path-perturbation to hit the probability kernel. It does not assume hyperbolicity but requires (either multiplicative or additive) noise. It extends the path-perturbation formula (or stochastic gradient method), the Bismut-Elworthy-Li formula, and a formula in Malliavin calculus (or likelihood ratio method). Then we derive a pathwise sampling algorithm and demonstrate it on the 40-dimensional Lorenz 96 system with noise. |
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3:00pm to 4:00pm - 510R Rowland Hall - Combinatorics and Probability Felix Clemen - (University of Victoria) Triangles in the Plane A classical problem in combinatorial geometry, posed by Erdos in 1946, asks to determine the maximum number of unit segments in a set of n points in the plane. Since then a great variety of extremal problems in finite planar point sets have been studied. Here, we look at such questions concerning triangles. Among others we answer the following question asked by |
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2:00pm to 3:00pm - RH 440R - Dynamical Systems David Damanik - (Rice University) Deterministic Delocalization We present joint work with Artur Avila on delocalizing Schr\"odinger operators in arbitrary dimensions via arbitrarily small perturbations of the potential. |