Search

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

Events for the weeks of April 19th – May 1st

Print these events

Tue, Apr. 21 1:25pm (online)	Algebra/Logic Jakub Rydval (TU Wien) View Online:https://cuboulder.zoom.us/j/96896272260 X In 2008, Bodirsky and Grohe showed that for every \Pi_n^P-level of the Polynomial Hierarchy (PH) there are omega-categorical Constraint Satisfaction Problems (CSPs) complete for this level. We show that, in fact, there are omega-categorical CSPs complete for any level of the PH. To this end, we use a recent result of Bodirsky, Kn\"{a}uer, and Rudolph for constructing omega-categorical CSPs from sentences of Monadic Second-Order logic (MSO) with certain preservation properties. As a secondary contribution, we develop a new tool for producing MSO sentences satisfying said preservation properties. In the present talk, I give an overview of the above-mentioned results and motivate several new questions. This is joint work with Santiago Guzman-Pro. The polynomial hierarchy and omega-categorical CSPs
Tue, Apr. 21 2:30pm (MATH 3…	Lie Theory Richard Green (CU) X A pair (g,k) of Lie algebras is a symmetric pair if k is the set of fixed points of an automorphism of g of order 2. We will show that when g and k are simply laced Lie algebras of equal rank, the pair gives rise to some combinatorial structures whose numerical invariants can be predicted in terms of matroids that are representable over the field with two elements. This is based on joint work with Tianyuan Xu (University of Richmond). Symmetric pairs and binary matroids
Wed, Apr. 22 2:10pm (Math350)	Math Phys Mudassir Moosa (CU Boulder Physics) TBA
Thu, Apr. 23 11am (MATH 220)	Functional Analysis Roberto Hernandez Palomares (University of Waterloo) X Spin models for singly-generated Yang-Baxter planar algebras are known to be determined by certain highly-regular classical graphs such as the pentagon or the Higman-Sims graph, which are extremely rare. Examples of spin models include the Jones and Kauffman polynomials. We will discuss the notion of higher-regularity for quantum graphs and give new examples of non-classical graphs yielding spin models. Time allowing, we will discuss some applications to quantum groups, topology and quantum information. Quantum graphs and spin models Sponsored by the Meyer Fund
Thu, Apr. 23 2:30pm (MATH 3…	Functional Analysis J. Quigg (Arizona State University) X One approach to identifying the C*-algebra of a product system over N^k is to build a representation of it with the aim of applying the Gauge-Invariant Uniqueness theorem. The main problem is how to build the representation. This is complicated by the commutativity of N^k - so many balanced tensor-product correspondences are isomorphic. I'll show how an abstract categorical result of Fowler-Sims can be used to surmount this obstacle. Joint work with Valentin Deaconu, Menevse Eryuzlu Paulovicks, and S. Kaliszewski. Use of monoidal categories to generate representations of product systems over N^k Sponsored by the Meyer Fund
Fri, Apr. 24 2:30pm (MATH 3…	PDE/Analysis Xueying Yu (Oregon State University) X This talk focuses on a fundamental concept in the field of partial differential equations - unique continuation principles. Such a principle describes the propagation of the zeros of solutions to PDEs. Specifically, it answers the question: what condition is required to guarantee that if a solution to a PDE vanishes on a certain subset of the spatial domain, then it must also vanish on a larger subset of the domain. Motivated by Hardy’s uncertainty principle, Escauriaza, Kenig, Ponce, and Vega were able to show in a series of papers that if a linear Schrödinger solution decays sufficiently fast at two different times, the solution must be trivial. In this talk, we will discuss unique continuation properties of solutions to higher-order Schrödinger equations and variable-coefficient Schrödinger equations, and extend the classical Escauriaza-Kenig-Ponce-Vega type of result to these models. This is based on joint works with S. Federico-Z. Li, and Z. Lee. Some unique continuation results for Schrödinger equations Sponsored by the Meyer Fund
Wed, Apr. 29 2:10pm (Math350)	Math Phys Gregory Berkolaiko (Texas A&M) TBA

Return to the top of the page