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Events for May – September 2016

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May. 17, 2016 11am (MATH 350)	Number Theory Amanda Tucker (University of Rochester) X What's the difference between 3, 1/3, the sum from n=1 to infinity of 1/n^3, and pi? We will start with a discussion of what it means for a number to be integral, rational, algebraic, or transcendental. We will talk about the history of the multiple zeta values (certain real numbers) and some open problems about them. You will leave this talk knowing more about the real numbers than you thought was possible, but also with more questions about the real numbers than you thought was possible! Multiple zeta values
May. 17, 2016 1pm (MATH 350)	Algebraic Geometry Amanda Tucker (University of Rochester) X We will introduce the area of arithmetic statistics and the Cohen- Lenstra heuristics. We will give some background about the work of Bhargava- Shankar-Tsimerman and Taniguchi-Thorne on the Davenport-Heilbronn theorems. We will then explain our recent proof that 96.2% of totally real cubic fields have genus number one and, if time permits, talk about some applications. This represents joint work with Kevin McGown. The arithmetic statistics of number fields
Jun. 01, 2016 2pm (Math 350)	Functional Analysis Sarah Reznikoff (Kansas State University) X In 1948 Naimark showed that the C-algebra of compact operators, K(H), has a unique irreducible representation and asked whether the converse is true; that is, must any C-algebra with this property be isomorphic to K(H)? We will out line the proof of Akemann and Weaver (2003) that the existence of a counterexample to Naimark's Problem is consistent with the axioms of set theory ZFC. Notes on the relative consistency of Naimark's Problem Sponsored by the Meyer Fund
Aug. 24, 2016 4pm (MATH 350)	Grad Student Seminar Boramey Chhay X So it's been a while since Calculus 3 and now you need to be able to answer student questions about it in the Help Lab. Not a problem! This talk will be a review of stuff from Calculus 3 that you may or may not have forgotten. All the Calc 3 you need for Help Lab
Aug. 30, 2016 12:10pm (MATH …	Kempner Janos Englander (CU Boulder) X Given a sequence of numbers in , consider the following experiment. First, we flip a fair coin and then, at step , we turn the coin over to the other side with probability , . What can we say about the distribution of the empirical frequency of heads as ? We show that a number of phase transitions take place as the turning gets slower (i.e. is getting smaller), leading first to the breakdown of the Central Limit Theorem and then to that of the Law of Large Numbers. It turns out that the critical regime is . Among the scaling limits, we obtain some well known special (Uniform, Gaussian, Semicircle and Arcsine) laws. The talk is intended to a general audience and no expertise in probability is assumed! This is joint work with S. Volkov (Lund, Sweden) Turning a coin instead of tossing it
Aug. 30, 2016 1pm (MATH 220)	Grad Algebra/Logic Agnes Szendrei (CU Boulder) X The Algebraic Dichotomy Conjecture predicts that the constraint satisfaction problem CSP(A) with a fixed finite template A is in P if the algebra associated to A has a Taylor term. (Otherwise, CSP(A) is known to be NP-complete.) The goal of this sequence of talks is to discuss a recent theorem of M. Olsak (Charles University) which greatly simplifies the condition "an algebra has a Taylor term". Namely, Olsak proved that if an algebra (finite or infinite) has a Taylor term, then it has a specific Taylor term in 12 variables. Taylor Terms, Part 1: Introduction
Sep. 06, 2016 1pm (MATH 220)	Grad Algebra/Logic Agnes Szendrei (CU Boulder) Taylor Terms, Part 2
Sep. 06, 2016 2pm (MATH 350)	Lie Theory Nat Thiem (CU) X The partition algebra is a classical example of a diagram algebra that contains many of the other famous combinatorial centralizer algebras as subalgebras. The search for a -analogue of these algebras leads to an investigation of the various coincidences that make the partition algebra combinatorially tractable. This talk gives an introduction to the partition algebra and discusses various ways to break its structure in attempted generalizations. Flavors of -partition algebras
Sep. 06, 2016 3pm (MATH 350)	Topology Markus Pflaum (CU Boulder Math) Organizational Meeting & Introduction to Derived Functors
Sep. 07, 2016 4pm (MATH 350)	Grad Student Seminar Paul Lessard X We'll begin by asking innocent questions; we'll confront the wildness of our assumptions; we'll build mathematics by abstacting epistemological principles in place of grand metaphysical assumptions; and we'll find out that the stuff of reason is space. We'll abstract human judgement and find that, "it's full of stars." Homotopy Type Theory is a new foundations for mathematics. HoTT synthesizes the intuitionism of Brouwer, Martin Lof's type theory ( a formal syntax for constructive mathematical reasoning ), Voevodsky's "construction" of a "small universe", Kant's contaposition of analytic and synthetic reason, and the Yoneda Lemma. An Idiosyncratic Introduction to Homotopy Type Theory and Synthetic Algebraic Topology
Sep. 13, 2016 12:10pm (MATH …	Kempner Peter Elliott (CU Boulder) X One hundred years ago, Ramanujan attached two conjectures to a function that he had defined when studying sums of integer squares. Time permitting I shall sweep over the twentieth century and indicate their ramifications in geometry, the automorphic world, classical and modern analytic and probabilistic number theory. Hopefully I shall reach recent results in which I, or Jonathan Kish and myself, have had a hand. Ramanujan's tau-function and something of what it provoked
Sep. 13, 2016 1pm (MATH 220)	Grad Algebra/Logic Jakub Oprsal (Charles University, Prague) X One way to measure term complexity of a finite algebra is to count how many symbols are needed to write down a term describing a particular n-ary term operation, and taking the maximum of these values among all n-ary term operations of the algebra. We will talk about algebras with a Mal'cev term for which there is a polynomial (in n) upper bound on these numbers. Term complexity in Mal'cev algebras
Sep. 13, 2016 2pm (MATH 220)	Jakub Oprsal (University of Krakow, Poland) X One of the ways to formulate the famous Taylor's modularity conjecture is the following: Suppose that we have two sets of identities in disjoint languages such that the variety described by its union has modular congruence lattices. Then one of the varieties described by either of the sets has modular congruences. We will discuss some ideas of a proof that the above is true for sets of identities implying that all the operations are idempotent (i.e., satisfy f(x,…,x) = x). Taylor's modularity conjecture
Sep. 13, 2016 2pm (MATH 350)	Lie Theory Jon Lamar (CU) X A supercharacter theory, S, of a group G is called characteristic if the action of Aut(G) on the lattice of supercharacter theories SCT(G) fixes S. I will provide a classification of the sublattice of characteristic supercharacter theories of the dihedral groups as well as discuss possible ways to characterize the remainder of the full lattice. Supercharacter theories of dihedral groups
Sep. 13, 2016 3pm (MATH 350)	Topology Markus Pflaum (CU Boulder Math) Introduction to Derived Functors - Part II
Sep. 14, 2016 4pm (MATH 350)	Grad Student Seminar Sebastian Bozlee X We will explain the results of "The Chaos Within Sudoku" by Maria Ercsey-Ravasz and Zoltan Toroczkai, in which Sudoku puzzles are solved using the unlikely tool of ordinary differential equations. The Chaos within Sudoku
Sep. 15, 2016 2pm (Math 350)	Functional Analysis Leonard Huang (CU Boulder) X In Part 1 of this series of two talks, which aims to explain the results of my dissertation, I will begin with a brief survey of Marc Rieffel’s theory of proper group actions on -algebras. I will then introduce Ralf Meyer’s extension of Rieffel’s work to the theory of square-integrable group actions on Hilbert -modules. In an attempt to generalize Meyer’s ideas so as to incorporate twisted group actions on -algebras, I was led to develop the category of Hilbert modules over a twisted -dynamical system, which will be the main focus of this talk. Generalized Fixed-Point Algebras for Twisted C*-Dynamical Systems (Part 1)
Sep. 20, 2016 10am (Math 350)	PDE/Analysis Taylor Joseph Klotz (CU Boulder) X This talk will be an attempt to introduce key concepts of using moving frames and exterior differential systems (EDS) to solve problems in differential geometry. Specific examples may include existence of conformal maps between surfaces and possibly a fun result on minimal surfaces in \mathbb{R}^3 depending on time. The talk will also omit many details for the sake of timely exposition. Looking at Geometry through a Frame
CANCELED Sep. 20, 2016	Lie Theory Sybille Schroll (University of Leicester) Special algebras Sponsored by the Meyer Fund
Sep. 20, 2016 3pm (MATH 220)	Topology Sebastian Bozlee (CU Boulder) Abelian Categories
Sep. 20, 2016 3pm (Math 350)	Algebraic Geometry Dan Edidin (University of Missouri) X Good quotients arise naturally in many contexts such as Geometric Invariant Theory. The good quotient of a smooth variety by an algebraic group is (etale) locally isomorphic to where is the tangent space at a point and is the stabilizer of the -action at . When all of the are finite then has finite quotient singularities and there is a well defined intersection product on the rational Chow groups of . However, when some of the are positive dimensional, the singularities of are worse. In this case very little is known about the intersection theory of . We explore an approach to intersection theory on good quotients which is based on strong cycles in equivariant Chow groups. (These will be defined in the talk). Strong embeddings and intersection products on good quotients Sponsored by the Meyer Fund
Sep. 21, 2016 4pm (MATH 350)	Grad Student Seminar Robert Hines X Didja know every positive integer is a sum of four squares? Nifty. We'll warm up by deciding which integers are representable as a sum of two squares using properties of the Gaussian integers, then mimic the process using similar properties of the Hurwitz quaternions. The only background assumed is some algebra (e.g. we'll be showing that every one-sided ideal of the Hurwitz quaternions is principal). Sums of Four Squares via the Hurwitz Equations
Sep. 27, 2016 10am (Math 350)	PDE/Analysis Pearce Washabaugh (CU Boulder) X Burger's equation is one of the basic model equations in fluid mechanics. In this talk I'll give an introduction to Burger's equation from the perspective of infinite dimensional geometry. We'll discuss how diffeomorphism groups can be endowed with a manifold structure and how with certain Riemannian metrics these groups have Burger's equation as their geodesic equations. We'll also see how different versions of Burger's equation that are simply related from the analytic perspective can have wildly different geometric properties. Studying Burger's Equation Through the Geometry of Diffeomorphism Groups
Sep. 27, 2016 12:10pm (MATH …	Kempner Pedro Berrizbeitia (Universidad Simon Bolivar) X Let be an integer. Except for finitely many primes , the equation has integer solutions and for all integer . The problem is a classical one in Number Theory. In fact, if is the number of solution of the equation, then . The analog problem for infinite or more general fields is the following: Let be a multiplicative group of finite index in , the multiplicative group of units of the field , what does look like, in particular, when is ?. The first publication on the subject appeard in 1989, when Leep and Shapiro, gave a positive answer when the index of in is 3. That is, they proved that except for a small and short list of exceptional fields. They conjectured that the result was true in the case of index 5, for any infinite field . They mentioned that they had not been succesfull even for , the rational numbers. In the talk we will prove that if is of finite index in , then , that is, every rational number is writen as the difference of two elements of . The proof is a very nice application of the Van der Waerden Theorem on artithmetic progressions, that we will state without proof. More general results in Ramsey Theory allow to prove the same result of any infinite field, and even for some other more general rings. We will brieffly describe these more general results and consequences. We will also discuss the behaviour of , of , etc. In fact, we will scketch the solution of a conjecture posed in 1992 by Bergelson and Shapiro on an additive question that was published in 2011, in a joint publication with Florian Luca. Additive properties of multiplicative groups of finite index in fields
Sep. 27, 2016 3pm (MATH 350)	Topology Nikki Sanderson (CU Boulder) Triangulated Categories
Sep. 29, 2016 2pm (Math 350)	Functional Analysis Leonard Huang (CU Boulder) X Part 2 of this series of two talks focuses on properties of twisted Hilbert -modules, which are seen as representations of twisted -dynamical systems. I will introduce Ralf Meyer’s bra-ket operators and use them to define the notion of a ‘square-integrable representation’. A construction of generalized fixed-point algebras for twisted -dynamical systems will then be given. The highlight of the talk will be a classification (up to isomorphism) of Hilbert modules over a fixed non-commutative torus purely in terms of Hilbert spaces with certain special properties. Generalized Fixed-Point Algebras for Twisted C*-Dynamical Systems (Part 2)
Sep. 29, 2016 3pm (MATH 350)	Probability Hakima Bessaih (University of Wyoming) X We study some models with microscale properties that are highly heterogeneous in space and time. The time variations are controlled by a stochastic particle dynamics described by a stochastic ODE (SDE). Our main results include the derivation of macroscale equations and showing that the macroscale equations are deterministic. We use the asymptotic properties of the SDE. The macro scale equations are derived through an averaging principle of the slow motion (fluid velocity) with respect to the fast motion (particle dynamics). Our results can be extended to more general nonlinear diffusion equations with heterogeneous coefficients. Homogenization of stochastic models in porous media
Sep. 30, 2016 4pm (MATH 350)	Grad Student Seminar Jae Min Lee X In this talk, we will discuss an infinite dimensional Riemannian geometric approach to the nonlinear wave equations and how this perspective provides additional insight into the properties of their solutions. To this end, we will first review finite dimensional Riemannian geometry and gently introduce the infinite dimensional version. Then we will reveal some concrete geometric interpretations of the Hunter-Saxton partial differential equation. It is inevitable to use vocabulary from differential geometry and functional analysis. But I will make sure to explain intuitive ideas with examples and maintain our focus on understanding the mathematical perspective rather than technicalities. An introduction to the geometric approach to PDEs

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