$University of Colorado Boulder$

Search

Algebraic Geometry DeLong Diversity Functional Analysis Geometry/Analysis Grad Algebra Seminar Kempner Lie Theory Logic MathClub Math Phys Noncomm Geometry Number Theory Probability Rep Theory Grad Student Seminar Thesis Defenses Topology Ulam Math Edu

Events for the weeks of September 19th – October 1st

Print these events

Tue, Sep. 21 1:50pm (Zoom)	Math Edu Emily Braley (Johns Hopkins University) X In this interactive session we will look back at some of the tools and techniques introduced earlier in the seminar from the MAA's Instructional Practices Guide. Participants will work together on problems in small groups and we will debrief on small group facilitation for the undergraduate classroom. Then, we will think about transforming traditional problems into more open ended questions that make space for exploration and discussion! Along the way we will highlight various teaching techniques that elicit student thinking and use student contributions. Activating the Classroom Practices
Wed, Sep. 22 4pm (Math 350)	MathClub Divya Vernerey (CU-Boulder) X We'll discuss some mental "tricks" like multiplying two-digit numbers in your head. In fact, there are simple mathematical principles behind these tricks. Of course, one can potentially use these math tricks to annoy siblings, family, and friends (warning: this might also lead to loss of friends). Magic of Mental Math: ways to annoy your siblings
Wed, Sep. 22 5pm (MATH 350)	Grad Student Seminar Andrew Campbell (CU Boulder) X There are three analysis courses every graduate student in our department has to take. In Real Analysis 1 and 2 we study measures, Lebesgue integration, L^p-spaces, Hilbert spaces, Fourier series, and differentiation. In Complex Analysis 1 we study holomorphic functions, complex integration, the Cauchy-Riemann equations, Cauchy's integral formula, and all of its wonderful consequences/applications. It is easy for a graduate student to go through these courses and never really consider that besides several integral symbols and the word analysis these two tracks do not actually have much overlap. In this talk we will go through a brief review/introduction to some of the topics above, discuss why the study of holomorphic functions appears so different from other areas of analysis, and describe some of the many connections between the two subjects. Party Hardy Spaces: An Introduction to Complex and Real Analysis
Thu, Sep. 23 3pm (virtual)	Probability Jonas Jalowy X The Circular Law states that the empirical eigenvalue distribution of non-Hermitian random matrices with independent entries will converge to the uniform distribution on the complex disk as the size of the matrix tends to infinity. In this talk, I will address the rate of convergence to the Circular Law in terms of a uniform Kolmogorov-like distance. The optimal rate of convergence is determined by matrices with Gaussian entries and is given by $n-1/2$ . Secondly, I will present that also matrices with non-Gaussian entries nearly attain this optimal rate. The method of proof involves a smoothing inequality for logarithmic polynomials. In a similar fashion, we will also discuss related models such as products of independent matrices and the empirical distribution of the roots of certain random polynomials with independent coefficients. The talk will contain numerous illustrations and numerical simulations supporting some open problems. Rate of convergence to the Circular Law and its powers
Tue, Sep. 28 1pm (Zoom)	Grad Algebra Seminar Peter Mayr (CU) X For relational structures A, B, the Promise Constraint Satisfaction Problem PCSP(A, B) asks whether a given input structure maps homomorphically to A or does not even map to B. We are promised that the input satisfies exactly one of these two cases. Note that if there exists C with homomorphisms A ? C ? B, then PCSP(A, B) reduces to CSP(C). All known tractable PCSPs seem to reduce to tractable CSPs in this way. However Barto (2019) showed that some PCSPs over finite structures require solving CSPs over infinite C. We provide examples showing that even when a reduction to finite C is possible, this structure may become arbitrarily large. This is joint work with Alexandr Kazda and Dmitriy Zhuk. Solving small PCSPs via large CSPs
Tue, Sep. 28 2pm (MATH 350)	Lie Theory Robert Muth (Washington & Jefferson College) X Khovanov-Lauda-Rouquier (KLR) algebras arise in the categorification theory of quantum groups. In affine type A, KLR representations can be studied through the lens of cuspidal modules, which categorify root vectors in PBW bases of the associated quantum group, or through the lens of Specht modules, associated with the cellular structure of cyclotomic KLR algebras. Cuspidal ribbons provide a sort of combinatorial bridge between these approaches. I will describe the combinatorics of cuspidal ribbon tableaux, as well as some implications they have in the world of KLR representation theory, such as providing bounding information on simple factors of Specht modules, as well as presentations of cuspidal modules. Cuspidal ribbon tableaux and representations of KLR algebras Sponsored by the Meyer Fund
Thu, Sep. 30 3pm (Zoom)	Probability Rodrigo Ribeiro (CU Boulder) TBA