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Events happening on October 9, 2018

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Oct. 09, 2018 11am (MATH 350)	Number Theory Daniel Martin (CU Boulder) X Continued fractions have been used since the late 19th century to produce rational approximations to complex numbers, but they are nonexistent outside of the five Euclidean imaginary quadratic fields. In this talk we will produce a tool that creates continued fractions in any imaginary quadratic field. We will also find applications of this tool to Bianchi group presentations and integral circle packings. The geometry of imaginary quadratic fields
Oct. 09, 2018 12:10pm (MATH …	Kempner Bram Mesland (Max Planck Institute for Mathematics Bonn) X Kasparov's KK-theory is a bivariant homology theory for C*-algebras providing a general framework for index theory. Cycles for the theory come from the abstract analogue of a first-order differential operator. After an exposition of the theory for non-specialists, I will discuss some recent results. These include analytic properties of self-adjoint operators, applications of KK-theory in the theory of arithmetic manifolds and automorphic forms and the physics of topological insulators. KK-theory in geometry and physics
Oct. 09, 2018 1pm (MATH 220)	Peter Mayr X We describe the second step of Zhuk's algorithm for solving CSP that combines local consistency methods and quotient algebras. CSP irreducibility
Oct. 09, 2018 2pm (MATH 350)	Lie Theory Farid Aliniaeifard (CU Boulder) X The concept of Hopf algebras originated from the theory of algebraic groups and algebraic topology in the mid 20th century and now it has many application in algebraic combinatorics. Also, the notion of a Hopf monoid in the monoidal category of linear species was introduced by Aguiar and Mahajan, and they show the great importance of this concept in algebraic combinatorics with examples that show many combinatorial objects have Hopf monoid structures. Hopf structures have numerous applications in many other mathematical branches, and now it is a familiar concept in representation theory as the class functions or superclass functions of some tower of groups have Hopf structures where representation theoretic functors give the product and coproduct. In this talk, we give a brief introduction to normal lattice supercharacter theories, and then we construct a Hopf structure by using these supercharacter theories. (With Nat Thiem and Shawn Burkett) Normal lattice supercharacter theories and Hopf structures
Oct. 09, 2018 2pm (MATH 220)	Michael Wheeler (CU Boulder) The existence of good ultrafilters
Oct. 09, 2018 3pm (MATH 350)	Ulam D. Kaledin X While deformation quantization first appeared in physics and/or differential geometry, there is actually a purely algebraic version of the story, and it has quite a lot of applications (for example, to algebraic geometry of symplectic singularities in the sense of Beauville). I will give a general introduction to the subject. I will mostly follow my old papers with Bezrukavnikov, but I will also present some newer results. Deformation quantization in algebraic geometry
Oct. 09, 2018 3pm (MATH 350)	Algebraic Geometry Dmitry Kaledin (Steklov Math Institute Moscow and University of Colorado) X While deformation quantization first appeared in physics and/or differential geometry, there is actually a purely algebraic version of the story, and it has quite a lot of applications (for example, to algebraic geometry of symplectic singularities in the sense of Beauville). I will give a general introduction to the subject. I will mostly follow my old papers with Bezrukavnikov, but I will also present some newer results. Deformation quantization in algebraic geometry
Oct. 09, 2018 4pm (MATH 350)	Topology Cherry Ng The Atiyah-Jänich Theorem and Kuiper's Theorem

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