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Events for August – December 2017

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Aug. 04, 2017 1pm (MATH 350)	Probability Jason Fulman (USC) X Many casinos routinely use mechanical card shuffling machines. We were asked to evaluate a new product, a shelf shuffler. This leads to new probability, new combinatorics and to some practical advice which was adopted by the manufacturer. The interplay between theory, computing, and real-world application is developed. This work is joint with Persi Diaconis and Susan Holmes Analysis of casino shelf shuffling machines
Aug. 30, 2017 4:03pm (MATH 3…	Grad Student Seminar Sebastian Bozlee X Generating functions are a tool that allow one to study sequences with power series. I will define the ordinary generating function of a sequence, then apply these generating functions to a few examples, including the Fibonacci numbers and the general solution of a linear homogeneous recurrence relation. A bit about generating functions
Sep. 01, 2017 1pm (MATH 350)	Init Conditions Sebastian Bozlee Intro to Categories, Part 1
Sep. 05, 2017 12:10pm (MATH …	Kempner David Stanovsky (Charles University Prague) X I will talk about the computational problem of knot recognition: given two knots, can one smoothly transform one into the other? I will show the method of arc coloring, which provides a large class of invariants of various strengths. For example, coloring can be used to obtain a certificate of unknottedness which can be verified in polynomial time. In the end, I will talk about the underlying algebraic structures, so called quandles, and their relation to the theory of permutation groups. A combinatorial approach to knot recognition
Sep. 05, 2017 2pm (MATH 350)	Lie Theory Farid Aliniaeifard (CU) X In 1911, Schur defined the Schur's Q functions in the studies of projective representations of symmetric groups. They showed great importance in many different contexts including representation of Lie superalgebras and certain cohomology classes, etc. Naturally, Stembridge generalized Schur's Q functions to peak algebra. It later appears that the Q functions and peak algebra are odd Hopf subalgebras of symmetric functions and quasi-symmetric functions respectively. In this talk, we will precisely give a definition of odd Hopf subalgebra for any combinatorial Hopf algebra. Then, we will provide a strategy to find the odd Hopf subalgebra of any combinatorial Hopf algebra. The odd Hopf subalgebra of a combinatorial Hopf algebra
Sep. 05, 2017 3pm (MATH 350)	Topology Agnès Beaudry (CU Boulder) Computations with the Adams Spectral Sequence
Sep. 06, 2017 4:03pm (MATH 3…	Grad Student Seminar Leo Herr A Proof from the Coloring Book
Sep. 08, 2017 1pm (MATH 350)	Init Conditions Sebastian Bozlee Intro to Categories, Part 2
Sep. 12, 2017 10am (Math 350)	Functional Analysis Andrzej Sitarz (Institute of Physics, Jagiellonian University in Kraków, Poland) X Quotient spaces of actions of finite groups on tori provide interesting examples of flat manifolds and orbifolds. In some cases, actions can also be defined on non-commutative tori, and the fixed-point sub-algebras give their non-commutative counterparts. I’ll discuss three-dimensional examples (non-commutative Bieberbach manifolds) and two-dimensional (the non-commutative pillow), addressing the question of whether the resulting objects are manifolds or orbifolds. Based on joint work with P. Olczykowski (Bieberbach manifolds) and T. Brzezinski (the non-commutative pillow). Quotients of Non-Commutative Tori
Sep. 12, 2017 1pm (MATH 220)	Peter Mayr (CU Boulder) X In combinatorial group theory the Reidemeister-Schreier Theorem (1927) asserts that a subgroup of finite index in a finitely presented group is itself finitely presented. Similar results exist for semigroups (Campbell, et al., 1996) and associative algebras over fields (Voden, 2009) for the appropriate interpretation of ``finite index''. We show a version for rings: let $B$ be a subring of a finitely presented ring $A$ such that $A/B$ is finitely generated as a group. Then $B$ is finitely presented. This is joint work with Nik Ruskuc (University of St. Andrews). Reidemeister-Schreier for rings 1
Sep. 12, 2017 2pm (MATH 350)	Lie Theory Farid Aliniaeifard (CU) X The maps from symmetric functions to Q functions and from quasi-symmetric functions to peak algebra, called Theta maps, are combinatorial Hopf morphisms and have their own interests. We are going to develop a general theory for theta maps for many families of combinatorial Hopf algebras. In particular, we will describe theta maps for the Malvenuto-Reutenaur Hopf algebra whose images are potentially generalizations of Q functions and peak algebra. We will also describe a Hopf algebra of permutations, which has a Theta map and the image is exactly the peak algebra. Theta maps for combinatorial Hopf algebras
Sep. 12, 2017 2pm (MATH 220)	Peter Mayr X In combinatorial group theory the Reidemeister-Schreier Theorem (1927) asserts that a subgroup of finite index in a finitely presented group is itself finitely presented. Similar results exist for semigroups (Campbell, et al., 1996) and associative algebras over fields (Voden, 2009) for the appropriate interpretation of ``finite index''. We show a version for rings: let $B$ be a subring of a finitely presented ring $A$ such that $A/B$ is finitely generated as a group. Then $B$ is finitely presented. This is joint work with Nik Ruskuc (University of St. Andrews). Reidemeister-Schreier for rings 2
Sep. 12, 2017 3pm (MATH 350)	Topology Paul Lessard X The talk is comprised of two obvious parts: In the first hour we will abstract the familiar "pasting lemma", defining sheaves, and discovering Grothendieck topologies as a minimal structure upon with a theory of sheaves might me built. In the subsequent hour we will discover how sheaves can be used not only to deal with geometry: structures consisting of continuous functions organized over the topology of the base; but may actually be used to organize and encode axioms about data which are not obviously geometric. In particular we will learn how sheaves with respect to different Grothendieck topologies on Joyal's category \Theta allow us to model a variety of generalizations of a category which are not merely -en vogue-, but at the heart of a new proof of the co-bordism hypothesis due to Ayala and Francis. Reverse Engineering Continuity from Sheaves, and Composition Laws Encoded as Sheaves: From Grothendieck Topologies to Globular Theories
Sep. 13, 2017 4:03pm (MATH 3…	Grad Student Seminar Leo Herr X Given a multiplication structure on a set, if we enlarge the set a little, how many new multiplications can we make that extend the old one? Metaphor: If we fatten a ring slightly, can we also fatten a given module? The principle of this talk is examples; the content is my own research with Jonathan Wise. I will define two words: "sheaf" and "exact," and explain what it is, exactly, that I do here. It should rely only on groups, rings, modules, and topological spaces, but more will be helpful. Mangled Modules: Sheaves, Exactness, and perversion
Sep. 15, 2017 1pm (MATH 350)	Init Conditions Sebastian Bozlee X We introduce universal properties through the example of products. Intro to Categories, Part 3
Sep. 19, 2017 1pm (MATH 220)	William DeMeo (CU Boulder) X We explore various aspects of the problem of representing a finite lattice as the congruence lattice of a finite algebra or an interval in the subgroup lattice of a finite group. We describe constructive methods that yield concrete representations, as well as some nonconstructive ways to prove existence of a representation. Minimal representations are discussed including computer programs to find them. These methods enable us to prove that every lattice with at most seven elements, with only one possible exception, has a representation as a congruence lattice of a finite algebra. This is joint work with Ralph Freese (U Hawaii) and Peter Jipsen (Chapman U). Representing finite lattices as congruence lattices of finite algebras
Sep. 19, 2017 2pm (MATH 350)	Lie Theory Richard Green (CU) X Lusztig's a-function is an integer-valued function on the elements of a Coxeter group, and it is defined in terms of the structure constants of the Kazhdan--Lusztig basis of the associated Hecke algebra. We call a Coxeter group "a(k)-finite" if it has finitely many elements with a-value equal to k. A Coxeter group element has a-value 1 if and only if it is "rigid", meaning that it has a unique reduced expression. The classification of a(1)-finite Coxeter groups is known, and this talk will describe the classification of a(2)-finite Coxeter groups. This is joint work with Tianyuan Xu (Queen's University). The classification of a(2)-finite Coxeter groups
Sep. 19, 2017 3pm (MATH 350)	Topology Sebastian Bozlee Stacks
Sep. 20, 2017 4:03pm (MATH 3…	Grad Student Seminar Leo Herr The Son of the Return of Mangled Modules: Redux
Sep. 22, 2017 1pm (MATH 350)	Init Conditions Leo Herr Manifolds
Sep. 26, 2017 10am (Math 350)	Functional Analysis Robin Deeley (CU Boulder) X I will introduce three examples of Smale spaces (Smale spaces are a class of hyperbolic dynamical systems). Group actions on these three examples will be introduced to motivate the study of group actions on a general Smale space. Finally, I will discuss such actions both in regard to a Smale space itself and the $C^{*}$ -algebras associated to it. This talk is based on joint work with Karen Strung. Smale Spaces and Group Actions on Them
Sep. 26, 2017 1pm (MATH 220)	Agnes Szendrei (CU Boulder) X We will discuss the following paradox: Let M be a strong idempotent linear Maltsev condition. Under mild restrictions on M the following statement is true: If A is a random finite algebra whose operations satisfy the identities in M, then asymptotically almost surely, A satisfies much stronger conditions than M. An example of a strong idempotent linear Maltsev condition is the condition ``There is a ternary operation m which satisfies the identities m(x,x,y)=y=m(y,x,x)''. Every group satisfies this condition with the (derived) operation m(x,y,z)=xy^{-1}z. Random finite algebras satisfying idempotent linear Maltsev conditions, Part 1
Sep. 26, 2017 2pm (MATH 350)	Lie Theory Richard Green (CU) X Lusztig's a-function is an integer-valued function on the elements of a Coxeter group, and it is defined in terms of the structure constants of the Kazhdan--Lusztig basis of the associated Hecke algebra. We call a Coxeter group "a(k)-finite" if it has finitely many elements with a-value equal to k. A Coxeter group element has a-value 1 if and only if it is "rigid", meaning that it has a unique reduced expression. The classification of a(1)-finite Coxeter groups is known, and this talk will describe the classification of a(2)-finite Coxeter groups. [This is a continuation of last week's talk, but it is not necessary to have attended the previous talk.] The classification of a(2)-finite Coxeter groups
Sep. 26, 2017 3pm (MATH 350)	Topology Markus Pflaum (CU Boulder) Introduction to Quantum Field Theory
Oct. 02, 2017 4pm (BESC 180)	DeLong Michael Hopkins (Harvard University) Homotopy theory and its many roles in mathematics
Oct. 03, 2017 11am (MATH 350)	Number Theory Qi Cheng (University of Oklahoma) X The Ring Learning-With-Errors (LWE) problem, whose security is based on hard ideal lattice problems, has proven to be a promising primitive with diverse applications in cryptography. There are however recent discoveries of faster algorithms for the principal ideal SVP problem, and attempts to generalize the attack to non-principal ideals. In this work, we study the LWE problem on group rings, and build cryptographic schemes based on this new primitive. One can regard the LWE on cyclotomic integers as a special case when the underlying group is cyclic, while our proposal utilizes non-commutative groups, which eliminates the weakness associated with the principal ideal lattices. In particular, we show how to build public key encryption schemes from Dihedral group rings, which maintains the efficiency of the ring-LWE and improves its security. LWE from Non-commutative Group Rings
Oct. 03, 2017 1pm (MATH 220)	Agnes Szendrei (CU Boulder) Random finite algebras satisfying idempotent linear Maltsev conditions, Part 2
Oct. 03, 2017 2pm (MATH 350)	Lie Theory No Talk Go to Delong.
Oct. 03, 2017 4pm (TBA)	DeLong Michael Hopkins (Harvard University) Topological quantum field theories
Oct. 10, 2017 10am (Math 350)	Functional Analysis Arlan Ramsay (CU Boulder) Decompositions of Polish Spaces and Measures on Them
Oct. 10, 2017 11am (MATH 350)	Number Theory Robert Benedetto (Amherst College) X Let $K$ be a number field, let $f∈ K(x)$ be a rational function of degree $d$ , and let $a∈ K$ . The roots of $fn(z)-a$ are the $n$ -th preimages of $a$ under $f$ , and they have the natural structure of a $d$ -ary rooted tree $T$ . There is a natural Galois action on the tree, inducing a representation of the absolute Galois group of $K$ in the automorphism group of $T$ . In many cases, it is expected that the image of this arboreal Galois representation has finite index in the automorphism group, but in some cases, such as when f is postcritically finite (PCF), the image is known to have infinite index. In this talk, we will present the first complete calculation of the arboreal Galois group of a PCF map, namely $f(z)=3z2-2z3$ , that is not induced by an endomorphism of an algebraic group. The arboreal Galois group of a PCF cubic polynomial
Oct. 10, 2017 12:10pm (MATH …	Kempner Robin Deeley (CU Boulder) X The Atiyah-Singer index theorem represents a landmark in 20th century mathematics. Since its proof in the 1960s, index theory has developed in many directions and found many applications. Understanding the index theorem is still nontrivial. However, there are a number of useful frameworks which make the Atiyah-Singer index theorem somewhat more intuitive. I will discuss one such framework, K-homology. K-homology is the homology theory dual to the cohomology theory K-theory. However, its usefulness in index theory comes from its various realizations (e.g., Baum-Douglas cycles, Fredholm cycles, extensions, etc), explicit isomorphisms between such realizations, and explicit pairings between such cycles and K-theory cocycles. Our main goal is to view the Atiyah-Singer index theorem as a corollary of the isomorphism between geometric and analytic K-homology. The Atiyah-Singer index theorem via K-homology: An introduction
Oct. 10, 2017 1pm (MATH 220)	Peter Mayr (CU Boulder) X Deciding whether the vertices of a given graph can be colored by 3 colors is well-known to be NP-complete. But how hard is it to distinguish between whether a graph can be colored by 3 colors or it cannot even be colored by 30 colors? This is an example of a Promise Constraint Satisfaction Problem (PCSP). There are only partial results on the complexity of PCSPs in general. We will present an algebraic approach for studying PCSP that uses a Galois connection between pairs of relational structures and their polymorphisms that is due to Brakensiek-Guruswami (2017) and Pippenger (2002). Promises and constraints 1
Oct. 10, 2017 2pm (MATH 350)	Lie Theory Mandi Schaeffer-Fry (Metro State) X Navarro has conjectured a necessary and sufficient condition for a finite group G to have a self-normalizing Sylow 2-subgroup, which is given in terms of the behavior of the ordinary irreducible characters of G under a specific Galois automorphism. Navarro-Tiep-Vallejo have conjectured a similar statement regarding groups whose Sylow 2-normalizers contain a single irreducible 2-Brauer character. Thanks to reduction theorems proved by myself and Navarro-Vallejo, respectively, a large part of the proofs of these conjectures is to understand the action of this Galois automorphism on characters of groups of Lie type. I will discuss the recent proof of these conjectures, including a description of the action of Galois automorphisms on characters of groups of Lie type. (Some portions of these results are joint work with J. Taylor.) On Galois Automorphisms Acting on Characters and Navarro's Sylow 2-Normalizer Conjectures
Oct. 10, 2017 2pm (MATH 220)	Peter Mayr (CU Boulder) Promises and constraints 2
Oct. 10, 2017 3pm (MATH 350)	Topology Leo Herr Topological Andre-Quillen homology
Oct. 11, 2017 4:03pm (MATH 3…	Grad Student Seminar Sarah Arpin X Elliptic curves are important sources of questions (and answers!) for mathematicians in number theory and algebraic geometry. The points of an elliptic curve have an "addition" operation, and the points of finite order with respect to this addition operation are called torsion points. This structure opens the door for even more questions, such as "what are the torsion points of an elliptic curve?" and "what do the components of these points look like?" This introductory talk will cover the definition of an elliptic curve with examples, the definition of the group law, and two main results regarding the torsion points of elliptic curves: the Nagell-Lutz Theorem and Mazur's Theorem. Proofs will be discussed as time allows. No prior knowledge of elliptic curves is required. Torsion points on elliptic curves
Oct. 17, 2017 10am (Math 350)	Functional Analysis Leonard Huang (CU Boulder) Bundles of Generalized Fixed-Point Algebras for Proper Groupoid Actions on $C^{*}$ -Algebras
Oct. 17, 2017 1pm (MATH 220)	Peter Mayr (CU Boulder) Promises and constraints 3
Oct. 17, 2017 2pm (MATH 350)	Lie Theory Henry Kvinge (CSU) X Khovanov-Lauda-Rouqiuer (KLR) algebras (also known as quiver Hecke algebras) were invented to categorify the negative half of quantum Kac-Moody algebras. It was later shown by Lauda-Vazirani that the simple modules of the cyclotomic KLR algebra, $R^{Λ}$ , carry the structure of the highest weight crystal $B(Λ)$ . It follows from this that combinatorial properties of $B(Λ)$ should be the shadow of module-theoretic properties of simple $R^{Λ}$ -modules. In classical affine type, highest weight crystals (which are infinite) have the remarkable property that they can be constructed from the tensor product of the much more tractable perfect crystals (which are finite). In this talk I will describe the algebraic analogue of this phenomenon in terms of simple $R^{Λ}$ -modules in the case where the perfect crystal is the Kirillov-Reshetikhin crystal $B1,1$ and $Λ$ is the fundamental weight $Λ_{i}$ . The Kirillov-Reshetikhin crystal $B1,1$ and cyclotomic quiver Hecke algebras
Oct. 17, 2017 3pm (MATH 350)	Topology Robin Deeley (CU Boulder) X In the 1980s, Baum and Douglas defined a geometric model for K-homology using spin^c manifolds. Through the isomorphism from geometric K-homology to analytic K-homology one can obtain the Atiyah-Singer index theorem. In the first half of the talk I will introduce both realizations of K-homology and this isomorphism. In the second half, an extension of this theory will be discussed. The starting point is Sullivan's notion of a Z/k manifold. Freed and Melrose proved an index theorem for operators acting on such spaces. We will consider a geometric model for K-homology with Z/k-coefficients where we replace the spin^c manifold theory used in the Baum-Douglas model with the corresponding theory for Z/k manifolds. The Freed-Melrose index theorem then plays the role that the Atiyah-Singer index theorem plays in the Baum-Douglas model. Geometric K-homology with Z/k-coefficients
Oct. 18, 2017 4:03pm (MATH 3…	Grad Student Seminar Brendt Gerics X History is written by the winners - and so it is with vector algebra. Around the turn of the 19th century, a battle was under way to construct a vector formalism to describe 3 dimensional Euclidean space. On one side there was Josiah Gibbs and Oliver Heaviside and the other side was William Clifford. The vector algebra of Gibbs and Heaviside prevailed and continues to dominate calculus classes today. The aim of this talk is to argue that Clifford's system, known as a Clifford algebra (also known as geometric algebra) is a superior formalism for such a task. In this talk, some basic definitions and constructions of Clifford algebras are presented, as well as some applications. Clifford the Big Red Algebra
Oct. 19, 2017 11am (MATH 350)	Geometry/Analysis Taylor Klotz (CU Boulder) X Equations of Lie type are ODEs on Lie groups that turn out to have their own version of a superposition formula. The usual result that a general solution to a linear system of ODEs can be written as a linear combination of homogenous and particular solutions turns out to be a special case of this idea. We'll explore the main theorem and go through some examples and possibly a proof. Applications to a special kind of connection in geometry may also be presented. Equations of Lie Type
Oct. 19, 2017 3pm (MATH 350)	Probability Clayton Shonkwiler (CSU) X In statistical physics, the basic (and highly idealized) model of a ring polymer like bacterial DNA is a closed random flight in 3-space with equal-length steps, often called an equilateral random polygon. While random flights without the closure condition are easy to simulate and analyze, the fact that the steps in a random polygon are not independent has made it challenging to develop practical yet provably correct sampling and numerical integration techniques for polygons. In this talk I will describe a geometric approach to the study of random polygons which overcomes these challenges. The symplectic geometry of the space of polygon conformations can be exploited to produce both Markov chain and direct sampling algorithms; in fact, this approach can be generalized to produce a sampling theory for arbitrary toric symplectic manifolds. This is joint work with Jason Cantarella, Bertrand Duplantier, and Erica Uehara. A Geometric Approach to Sampling Loop Random Flights
Oct. 24, 2017 1pm (MATH 220)	Agnes Szendrei (CU Boulder) Local term operations on ultrapowers, Part 1
Oct. 24, 2017 2pm (MATH 350)	Lie Theory Shawn Burkett (CU) X One common definition of a (finite) nilpotent group is that a group is nilpotent if and only if it has a central series which terminates in the trivial group. By defining appropriate analogs of the center and commutator subgroups, one may define central series for each supercharacter theory $S$ of a finite group $G$ . If there is a central series for $S$ which terminates in the trivial group, we will say that $G$ is $S$ -nilpotent. The concept of $S$ -nilpotence is a generalization of nilpotence in the sense that $S$ -nilpotence implies nilpotence and the two notions agree when $S$ is the finest supercharacter theory of $G$ . In this talk, we will describe the structure of those supercharacter theories $S$ for which $G$ is $S$ -nilpotent and show that when $G$ is $S$ -nilpotent, a number of familiar properties of $G$ hold and can be deduced from the supercharacter table of $S$ . We will also give several characterizations of $S$ -nilpotence as well as an analog of Fitting's theorem. A supercharacter theory version of nilpotence
Oct. 24, 2017 2pm (MATH 220)	Agnes Szendrei (CU Boulder) Local term operations on ultrapowers, Part 2
Oct. 24, 2017 3pm (MATH 350)	Kempner Peter May (University of Chicago) X From P.A. Smith to the present. Around 80 years ago, Smith proved the remarkable result that if a finite $p$ -group $G$ acts on a compact space $X$ that has the mod $p$ homology of a sphere, then the fixed point space $X^{G}$ also has the mod $p$ homology of a sphere. Equivariant algebraic topology has developed in fits and starts ever since. I'll give some glimpses of current directions and questions. Glimpses of equivariant algebraic topology
Oct. 24, 2017 4pm (MATH 350)	Topology Peter May (UChicago) X I will review an ancient approach to nonequivariant infinite loop space theory and describe how it generalizes equivariantly. (I will not assume any prior knowledge of this area of mathematics.) Glimpses of equivariant infinite loop space theory
Oct. 25, 2017 5pm (Math 350)	MathClub Janos Englander (CU Boulder) X Following the very popular talk given by Dr. Hanin in the Math Club some time ago, we are now asking ourselves “why buses always seem to run more frequently in the opposite direction,” and further, puzzling questions from probability theory. Why buses always seem to run more frequently in the opposite direction
Oct. 26, 2017 11am (MATH 350)	Geometry/Analysis Taylor Klotz (CU Boulder) Equations of Lie Type, Part 2
Oct. 31, 2017 12:10pm (MATH …	Kempner Emily Gari (CU Boulder) X Emily Gari, the Gemmill Engineering, Math & Physics Library’s Math Liaison Librarian, will provide an overview of library resources & services and literature review techniques, and answer any and all library related questions. Overview of Library Research
Oct. 31, 2017 2pm (MATH 350)	Lie Theory Megan Ly and Shawn Burkett (CU) X Schur--Weyl duality is a fundamental framework in combinatorial representation theory. It intimately relates the irreducible characters of the symmetric group to the irreducible characters of the general linear group via their commuting actions on tensor space. We investigate the analog of Schur-Weyl duality for the group of unipotent upper triangular matrices over a nite eld. In this case, the character theory of these upper triangular matrices is unattainable. Thus we employ a generalization, known as supercharacter theory, to create a striking variation on the character theory of the symmetric group with combinatorics based on set partitions. We present a combinatorial structure that encodes the decomposition of a tensor space into supercharacters in order to describe the maps that centralize the action of the group of unipotent upper triangular matrices. AND A supercharacter theory of a nite group is an approximation of its character theory where the role of the irreducible characters is played by a certain set of characters, called supercharacters, which enjoy some similar algebraic properties. Given a supercharacter theory of $G$ , a lattice of normal subgroups of $G$ can be associated via the kernels of the supercharacters. Conversely, given any lattice $ℒ$ of normal subgroups of $G$ , a supercharacter theory of $G$ can be constructed whose associated lattice is $ℒ$ and which is as coarse as possible, in some sense. In this talk, we will discuss some properties of these lattices, as well as the possibility of constructing finer supercharacter theories from a lattice of normal subgroups by specifying supercharacter theories on each covering relation. Schur--Weyl Duality for Unipotent Upper Triangular Matrices AND Lattices of normal subgroups and supercharacter theory
Oct. 31, 2017 3pm (MATH 350)	Topology Katharine Adamyk TBA
Nov. 02, 2017 11am (MATH 350)	Geometry/Analysis Congming Li (CU Boulder, Applied Math) X First, we give a brief introduction on the central role played by a priori estimates in PDE analysis. We then present some Liouville type theorems via blowing-up arguments to establish some important a priori estimates. We also plan to present some related maximum principle type theorems. A priori estimates--the core of PDE analysis
Nov. 07, 2017 10am (Math 350)	Functional Analysis Robin Deeley (CU Boulder) X The stable $C^{}$ -algebra of a Smale space is obtained from the étale groupoid associated to the space’s stable equivalence relation. When the original system is mixing, the stable $C^{}$ -algebra is simple, separable, nuclear and stably finite. I will outline the construction of an explicit inductive-limit decomposition of the stable $C^{}$ -algebra when the stable sets are totally disconnected. From this, one can often compute the $K$ -theory of the stable $C^{}$ -algebra. The talk will be example-based. In particular, no knowledge of Smale spaces is required. This talk is based on joint work with Allan Yashinski. The Structure of the Stable $C^{*}$ -Algebra of a Class of Smale Spaces
Nov. 07, 2017 11am	Number Theory Amy Feaver (King's University) X (Joint with Anna Puskas) In this talk, we determine all of the imaginary $n$ -quadratic fields with class number dividing 32, $n>1$ ; results for $n=1$ were previously computed by Watkins. Our results provide techniques to find complete lists of imaginary $n$ -quadratic fields of class number $2m$ for nonnegative integers $m$ . Further, given a fixed $m>0$ we find a bound $B(m)$ on $n$ for which there are no imaginary $n$ -quadratic fields of class number $2m$ whenever $n>B(m)$ . Imaginary Multiquadratic Fields of Class Number Dividing 32
Nov. 07, 2017 1pm (MATH 220)	Peter Mayr (CU Boulder) Promises and constraints 4
Nov. 07, 2017 3pm (Math 350)	Kempner Kathryn Hess (EPFL) X I will describe results obtained in collaboration with the Blue Brain Project on the topological analysis of the structure and function of digitally reconstructed microcircuits of neurons in the rat cortex. The topology of the microconnectome
Nov. 07, 2017 4pm (MATH 350)	Topology Kathryn Hess (EPFL) X I will explain the construction of a new model for the configuration space of a product of two closed manifolds in terms of the configuration spaces of each factor separately. The key to the construction is the lifted Boardman-Vogt tensor product of modules over operads, developed earlier in joint work with Dwyer. (Joint work with Bill Dwyer and Ben Knudsen.) Configuration spaces of products Sponsored by the Meyer Fund
Nov. 08, 2017 4:03pm (MATH 3…	Grad Student Seminar Sarah Arpin X TBD TBD
Nov. 08, 2017 5pm (Math 350)	MathClub Keith Kearnes (CU Boulder) X I will talk about how algebra can be used to classify the hardness of complexity problems. Algebra and Algorithms
Nov. 14, 2017 10am (Math 350)	Functional Analysis Leonard Huang (CU Boulder) X In a 1999 paper, Alex Kumjian and David Pask proved that if a discrete group $G$ acts freely on a directed graph $F$ , and if $α$ denotes the induced action of $G$ on the $C^{}$ -algebra $C(F)$ of the graph, then the reduced crossed-product $Cr(G,C(F),α)$ is strongly Morita-equivalent to the $C^{}$ -algebra $C(F/G)$ of the quotient graph. Very recently, Valentin Deaconu has been studying actions of discrete groupoids on Cuntz-algebra graphs, where the vertex set of such a graph is precisely the unit space of the acting groupoid. In this talk, I shall explain my observation that Jonathan Brown’s theory of proper groupoid dynamical systems may be used to prove an analog of the Kumjian-Pask Theorem for free actions of discrete groupoids on Cuntz-algebra graphs (in the sense of Deaconu). A Kumjian-Pask Theorem for Free Actions of Discrete Groupoids on Cuntz-Algebra Graphs
Nov. 14, 2017 11am (MATH 350)	Number Theory Scott Ahlgren (UIUC) X Kloosterman sums are ubiquitous in number theory. We estimate sums of Kloosterman sums of half-integral weight. Our estimates are uniform in all parameters in analogy with Sarnak and Tsimerman’s improvement of Kuznetsov's bound for the ordinary Kloosterman sums. As an application, we obtain an improved estimate for the classical problem of estimating the size of the error term in Rademacher's famous formula for the partition function. This is joint work with Nick Andersen (UCLA) Kloosterman sums, Maass cusp forms, and Rademacher’s formula
Nov. 14, 2017 12:10pm (Math …	Kempner Josh Grochow (CU Boulder) X Wildness is a phenomenon that grew up in representation theory, but has broad implications for classification problems, and turns out to be at the mathematical core of several major open problems in computational complexity. To give the flavor: Drozd's Dichotomy Theorem says that any finite-dimensional associative algebra over a field either has: (a) only finitely many indecomposable representations (e.g., finite groups in characteristic zero), (b) only finitely many 1-parameter families of indecomposable representations of each dimension (e.g., the polynomial ring k[x], where the 1-parameter families are given by choosing an eigenvalue for a Jordan block), or (c) is so complicated that it "contains" the representations of all other finite-dimensional algebras. The latter are called wild. This talk will provide a relatively gentle* introduction to wildness, and a few of the many places it arises in mathematics and computational complexity, including algorithms for testing isomorphism of finite groups, algorithms for multiplying matrices, and the only current approach to resolving major open questions such as P versus NP. * - In particular, by "gentle" I mean that I will not assume any background in representation theory. Wildness & geometry in representation theory & computational complexity
Nov. 14, 2017 1pm (MATH 220)	Athena Sparks (CU Boulder) Polynomial-time algorithm for PCSPs with majority polymorphisms
Nov. 14, 2017 2pm (MATH 350)	Lie Theory Farid Aliniaeifard (CU) X We introduce a new class of polytopes generalizing chain polytopes of posets introduced by Stanley. More precisely, we define a polytope for each (non-reflexive) relation R on a finite set X. The vertices of the polytopes are indexed by the independent sets for the relation, which are natural generalizations of the notion of an antichain in a poset. Part of the motivation for studying this class of polytopes is the variety of polytopes that it encompasses. These include polytopes whose vertices are indexed by partitions, noncrossing partitions, nonnesting partitions. We describe the 1-skeletons of these polytopes and show that the 2-faces are either triangles or quadrilaterals. In the end, we define the Birkhoff R-polytope and describe its 1skeletons. R-Polytopes
Nov. 14, 2017 2pm (MATH 220)	Peter Mayr (CU Boulder) Promises and constraints 5
Nov. 14, 2017 3pm (MATH 350)	Topology Andy Riddle X Abstract: In the 1960’s Quillen developed model categories as a way to axiomatize homotopy theory. In this setup, a Quillen model category is a category with three special classes of morphism (weak equivalences, fibrations, and cofibrations) which satisfy a few axioms. These axioms then give a framework in which it is possible to setup the machinery of homotopy theory in a wide variety of contexts. In this talk I will give a gentle introduction to the definition of a model category and consider some of the model category structures which occur most frequently in algebraic topology. Introduction to Model Categories
Nov. 15, 2017 4:03pm (MATH 3…	Grad Student Seminar Sebastian Bozlee X Solutions to polynomial equations are most easily found in affine space, $\C^n$, but a better place to study them is projective space. We will use the problem of where parallel lines intersect to arrive at a definition of projective space, then take a look around this new world with the help of a pair of computer programs written by the speaker. A look into projective space
Nov. 16, 2017 3pm (MATH 350)	Probability Yu-Jui Huang (CU Boulder) X For time-inconsistent control/stopping problems, it is known that one should employ an equilibrium strategy, formulated in an intertemporal game between current and future selves. Such strategies, however, are not unique. This gives rise to two unsettled problems: (i) How do we find all equilibria? (ii) If we found all equilibria, how do we select the appropriate one to use? For stopping problems under non-exponential discounting, we develop a new method, called the iterative approach, to resolve both (i) and (ii). First, we formulate equilibria as fixed points of an operator, which represents strategic reasoning that takes into account future selves’ behaviors. Under appropriate regularity conditions, every equilibrium can be found through a fixed-point iteration. When the state process is one-dimensional, we further establish the existence of an optimal equilibrium, which generates larger value than any other equilibrium does at all times. To the best of our knowledge, this is the first time a dominating subgame perfect Nash equilibrium is shown to exist in the literature of time-inconsistency. Our theory is illustrated explicitly in several real options models. Optimal Equilibrium for Time-inconsistent Stopping Problems
Nov. 28, 2017 10am (Math 350)	Functional Analysis Elmar Wagner (Instituto de Física y Matemáticas Universidad Michoacana de San Nico…) X One of the most frequent relations appearing in quantum-group theory is $x y = q y x$ , where $q$ denotes a real deformation parameter. Defining a $$ -structure by $x := y$ , one obtains the relation for the quantum complex plane: $x x = q x x$ . Operator theorists call Hilbert-space operators satisfying this equation “ $q$ -normal operators”. It is known that $q$ -normal operators are never bounded. To study such quantum spaces in the $C^{}$ -algebraic setting, one may apply Woronowicz’s theory of $C^{}$ -algebras generated by unbounded elements. It turns out that these quantum spaces can be described by subalgebras of certain crossed-product $C^{}$ -algebras. In this talk, I will give a complete topological description of the $C^{}$ -algebras generated by $q$ -normal operators, including their $K$ -theory, $K$ -homology and index pairings. Among all these $C^{}$ -algebras, there is only one that has the same $K$ -theoretical behavior as its classical counterpart. This happens if and only if the spectrum of $\|x\|$ is the entire positive half-line. (Joint work with Ismael Cohen.) $C^{*}$ -Algebras Generated by the Quantum Complex Plane Sponsored by the Meyer Fund
Nov. 28, 2017 11am (MATH 350)	Number Theory Robert A. Hines (CU) X We will recall two characterizations of badly approximable real numbers (via continued fractions and geodesic trajectories on the modular surface) and discuss real quadratic irrationals from both perspectives. We will then generalize these characterizations to imaginary quadratic fields (using continued fractions when applicable and geodesic trajectories in the Bianchi orbifolds more generally). Finally we will use these characterizations to produce examples of badly approximable numbers (those lying on anisotropic rational circles). These examples include algebraic numbers of every even degree over the rationals. Badly approximable numbers over imaginary quadratic fields
Nov. 28, 2017 12:10pm (MATH …	Kempner Alexander Hulpke (CSU Fort Collins) X The group $SLn(Z)$ (as well as many of its friends) is ubiquitous in Algebra, Number Theory or Geometry. For $n≥ 3$ it has the congriuence subgroup property, meaning that any finite index subgroup $U$ contains the kernel of a ``reduction by m’’ homomorphism $colon SLn(Z)→ SLn(Z/mZ)$ ’’. The smallest $m$ with this property is called the level of $U$ . For a subgroup $U$ , given by generators, we want to compute its level (which then allows to compute index and test membership efficiently). This task consists of two parts: Determining the primes dividing $m$ and then the power of each prime. Using the structure of SL over residue class rings $Z/kZ$ , the latter can be computed in finite congruence images. For the former we utilize the generic description of maximal subgroups of SL according to Aschbacher classes and develop effective tests for determining those primes, for which the congruence image lies in a particular congruence image. This is joint work with Alla Detinko (St Andrews) and Dane Flannery (Galway) Finding the level of arithmetic subgroups of SL_n
Nov. 28, 2017 1pm (MATH 220)	Nik Ruskuc (St Andrews) X It has become a folk-lore in group theory that subgroups of finite index share many basic properties with their parent group. For instance, Schreier's Theorem asserts that a subgroup H of finite index in a group G is finitely generated if and only if G is finitely generated. One can replace 'finitely generated' by 'finitely presented' (Reidemeister-Schreier Theorem), 'residually finite', etc. Motivated by the generality, ubiquity and importance of these types of results, one may be tempted to look for analogues in other algebraic systems. In this talk I will concentrate on such analogues for the Schreier and Reidemeister-Schreier theorems in rings and semigroups. It turns out that for rings both theorems carry over, and generalise to K-algebras over noetherian commutative rings. However, the proof exhibits some significant differences from the original group result. For semigroups, even the meaning of 'index' comes into question, but then it turns out that one can prove several different types of the above results, e.g. for subgroups of semigroups, or for Schutzenberger groups, or for subsemigroups of finite complement. I will conclude with some open problems arising from the comparison between rings and semigroups. The ring version of the Reidemeister-Schreier Theorem is recent joint work with Peter Mayr. Finite index and finiteness conditions: Groups and Semigroups Sponsored by the Meyer Fund
Nov. 28, 2017 2pm (MATH 350)	Lie Theory Jon Lamar (CU) X TBD Two Hopf subalgebras from restriction supercharacter theories
Nov. 28, 2017 2pm (MATH 220)	Nik Ruskuc (St Andrews) X It has become a folk-lore in group theory that subgroups of finite index share many basic properties with their parent group. For instance, Schreier's Theorem asserts that a subgroup H of finite index in a group G is finitely generated if and only if G is finitely generated. One can replace 'finitely generated' by 'finitely presented' (Reidemeister-Schreier Theorem), 'residually finite', etc. Motivated by the generality, ubiquity and importance of these types of results, one may be tempted to look for analogues in other algebraic systems. In this talk I will concentrate on such analogues for the Schreier and Reidemeister-Schreier theorems in rings and semigroups. It turns out that for rings both theorems carry over, and generalise to K-algebras over noetherian commutative rings. However, the proof exhibits some significant differences from the original group result. For semigroups, even the meaning of 'index' comes into question, but then it turns out that one can prove several different types of the above results, e.g. for subgroups of semigroups, or for Schutzenberger groups, or for subsemigroups of finite complement. I will conclude with some open problems arising from the comparison between rings and semigroups. The ring version of the Reidemeister-Schreier Theorem is recent joint work with Peter Mayr. Finite index and finiteness conditions: Rings Sponsored by the Meyer Fund
Nov. 28, 2017 3pm (Math 350)	Algebraic Geometry Michael Fried (UC Irvine) X This seminar consists of two consecutive talks (3-4 pm and 4-5 pm). First talk 3-4 pm Title: What Gauss Told Riemann About Abel's Theorem, Part 1: Tools from understanding rational functions in 1 complex variable Abstract: There are two exceedingly famous Abel Theorems. The more well-known, and easier, describes the "abelian (analytic) functions" on a compact complex 1-dimensional torus. The other bundles together all those complex tori, with their prime degree isogenies. Riemann's generalization of the first features his famous theta functions. His deepest work aimed at generalizing Abel's second theorem. He died too young to fulfill the whole vision. We can see how such a generalization works, and its relation to modern problems, by considering how Galois used Abel's spaces to produce simple groups (the opposite of solvable) from algebraic functions. In this first lecture, I introduce tools using just rational functions in 1-variable (like those that appeared in high school algebra). I will conclude with a Proposition, that introduces Braids for a formula to calculate the genus, in particular, of Abel's spaces. Second talk 4-5 pm Title: What Gauss Told Riemann About Abel's Theorem, Part 2: Abel's spaces in towers, and how those towers generalize Abstract: Abel's spaces are level 0 of a tower of spaces we now label as {X_0(pk+1)}k=0^{infty} (modular curves). I will use rational functions to produce this tower. Then, almost without lifting my chalk from the blackboard, I will give such towers using (essentially) any finite group G that isn't nilpotent (product of its p-Sylows) and has r = 4 generating conjugacy classes. Like modular curves, we see each tower level is an upper half-plane quotient, ramifying at the points (0, 1, infty) over the famous copy of Riemann's sphere, the j-line. The braid formula applies to computing their genuses, too. Yet, except for special groups G, the tower levels are not modular curves. I will do one example, G = A5 (the alternating group of degree 5), where we clearly see these are not modular curves. The same construction applies for any value of r. For all r, these spaces have properties that generalize famous results about modular curves, and those interpret as statements about The Inverse Galois Problem. These lectures introduce a book I am completing: Monodromy, l-adic Representations and The Regular Inverse Galois Problem. What Gauss Told Riemann About Abel's Theorem
Nov. 28, 2017 3pm (MATH 350)	Number Theory Michael Fried (UC Irvine) X This seminar consists of two consecutive talks (3-4 pm and 4-5 pm). First talk 3-4 pm Title: What Gauss Told Riemann About Abel's Theorem, Part 1: Tools from understanding rational functions in 1 complex variable Abstract: There are two exceedingly famous Abel Theorems. The more well-known, and easier, describes the "abelian (analytic) functions" on a compact complex 1-dimensional torus. The other bundles together all those complex tori, with their prime degree isogenies. Riemann's generalization of the first features his famous theta functions. His deepest work aimed at generalizing Abel's second theorem. He died too young to fulfill the whole vision. We can see how such a generalization works, and its relation to modern problems, by considering how Galois used Abel's spaces to produce simple groups (the opposite of solvable) from algebraic functions. In this first lecture, I introduce tools using just rational functions in 1-variable (like those that appeared in high school algebra). I will conclude with a Proposition, that introduces Braids for a formula to calculate the genus, in particular, of Abel's spaces. Second talk 4-5 pm Title: What Gauss Told Riemann About Abel's Theorem, Part 2: Abel's spaces in towers, and how those towers generalize Abstract: Abel's spaces are level 0 of a tower of spaces we now label as {X_0(pk+1)}k=0^{infty} (modular curves). I will use rational functions to produce this tower. Then, almost without lifting my chalk from the blackboard, I will give such towers using (essentially) any finite group G that isn't nilpotent (product of its p-Sylows) and has r = 4 generating conjugacy classes. Like modular curves, we see each tower level is an upper half-plane quotient, ramifying at the points (0, 1, infty) over the famous copy of Riemann's sphere, the j-line. The braid formula applies to computing their genuses, too. Yet, except for special groups G, the tower levels are not modular curves. I will do one example, G = A5 (the alternating group of degree 5), where we clearly see these are not modular curves. The same construction applies for any value of r. For all r, these spaces have properties that generalize famous results about modular curves, and those interpret as statements about The Inverse Galois Problem. These lectures introduce a book I am completing: Monodromy, l-adic Representations and The Regular Inverse Galois Problem. What Gauss told Riemann about Abel's theorem
Nov. 28, 2017 3pm (MATH 350)	Topology Michael Fried (UC Irvine) X This seminar consists of two consecutive talks (3-4 pm and 4-5 pm). First talk 3-4 pm Title: What Gauss Told Riemann About Abel's Theorem, Part 1: Tools from understanding rational functions in 1 complex variable Abstract: There are two exceedingly famous Abel Theorems. The more well-known, and easier, describes the "abelian (analytic) functions" on a compact complex 1-dimensional torus. The other bundles together all those complex tori, with their prime degree isogenies. Riemann's generalization of the first features his famous theta functions. His deepest work aimed at generalizing Abel's second theorem. He died too young to fulfill the whole vision. We can see how such a generalization works, and its relation to modern problems, by considering how Galois used Abel's spaces to produce simple groups (the opposite of solvable) from algebraic functions. In this first lecture, I introduce tools using just rational functions in 1-variable (like those that appeared in high school algebra). I will conclude with a Proposition, that introduces Braids for a formula to calculate the genus, in particular, of Abel's spaces. Second talk 4-5 pm Title: What Gauss Told Riemann About Abel's Theorem, Part 2: Abel's spaces in towers, and how those towers generalize Abstract: Abel's spaces are level 0 of a tower of spaces we now label as {X_0(pk+1)}k=0^{infty} (modular curves). I will use rational functions to produce this tower. Then, almost without lifting my chalk from the blackboard, I will give such towers using (essentially) any finite group G that isn't nilpotent (product of its p-Sylows) and has r = 4 generating conjugacy classes. Like modular curves, we see each tower level is an upper half-plane quotient, ramifying at the points (0, 1, infty) over the famous copy of Riemann's sphere, the j-line. The braid formula applies to computing their genuses, too. Yet, except for special groups G, the tower levels are not modular curves. I will do one example, G = A5 (the alternating group of degree 5), where we clearly see these are not modular curves. The same construction applies for any value of r. For all r, these spaces have properties that generalize famous results about modular curves, and those interpret as statements about The Inverse Galois Problem. These lectures introduce a book I am completing: Monodromy, l-adic Representations and The Regular Inverse Galois Problem. What Gauss told Riemann about Abel's theorem
Nov. 30, 2017 11am (MATH 350)	Geometry/Analysis Dana Mendelson (Chicago) X We consider the (de)focusing cubic Gross-Pitaevskii (GP) hierarchy on R, which is an infinite hierarchy of coupled linear non-homogeneous PDE which appears in the derivation of the cubic nonlinear Schrodinger (NLS) equation from quantum many-particle systems. Motivated by the fact that the cubic NLS on R is an integrable equation which admits infinitely many conserved quantities, we exhibit an infinite sequence of operators which generate analogous conserved quantities for the GP hierarchy. This is joint work with Andrea Nahmod, Natasa Pavlovic, and Gigliola Staffilani. An infinite sequence of conserved quantities for the cubic Gross-Pitaevskii hierarchy on R Sponsored by the Meyer Fund
Nov. 30, 2017 3pm (MATH 350)	Probability Rafael Frongillo (CU Boulder) X In statistics, the term "elicitation" refers to the relationship between a loss function and its (expected) minimizer. The term arises from economics, where the loss is taken to be a monetary penalty, and one wishes to incentivize someone to truthfully report a desired statistic of some eventually observed random variable. Interestingly, not all statistics are elicitable, including simple measures of risk or deviation like the variance of a random variable. I will give a brief overview of elicitation, and mention a few interesting open questions in elicitation complexity, where we seek to indirectly elicit otherwise non-elicitable statistics. I will conclude with a connection to the notion of random individual sequences. Elicitation Complexity and Individual Sequences
Dec. 05, 2017 1pm (MATH 220)	Jeff Shriner (CU Boulder) X The Subpower Membership Problem for a fixed finite algebra A (SMP(A)) is a combinatorial decision problem which asks, given a set of generators a_1,...,a_n and a distinguished tuple b in a direct power of A, is b in the subalgebra generated by a_1,...,a_n? In this talk, we discuss a construction which begins with any finite algebra A, and ends with a structurally 'nicer' algebra B for which SMP(B) is at least as hard as SMP(A). Given a specific finite algebra A, it is then natural to ask if the complexity of the associated problem SMP(B) is equal to or harder than SMP(A). We will look at a known example of a finite semigroup S for which SMP(S) is NP-complete, and show that the subpower membership problem for the associated 'nicer' algebra is also NP-complete. An NP-Complete Example for the Subpower Membership Problem
Dec. 05, 2017 2pm (MATH 350)	Lie Theory Josh Grochow (CU) X How hard it is to multiply matrices is a central open question in computational complexity, with ties to algebraic geometry and representation theory. In this talk I'll survey some recent work on matrix multiplication which brings together algorithms, representation theory, and additive combinatorics. Highlights include a transparent proof (joint with C. Moore) of Strassen's original 1969 algorithm for matrix multiplication - which was the first to beat $O(n3)$ steps - and using ideas from the resolution of the Cap Set Conjecture to deepen our understanding of the Cohn-Umans group-theoretic approach to matrix multiplication (joint with J. Blasiak, T. Church, H. Cohn, E. Naslund, W. F. Sawin, and C. Umans). Representation theory and additive combinatorics in algorithms for matrix multiplication
Dec. 05, 2017 2pm (MATH 220)	Trevor Jack (CU Boulder) X A semigroup S is nilpotent if S^n = 0 for some n. We describe a polynomial-time algorithm for determining whether a semigroup of transformations given by generators is nilpotent. Checking nilpotence for semigroups
Dec. 05, 2017 3pm (MATH 350)	Topology Nikki Sanderson X Time series analysis traditionally relies upon statistics and frequency analyses that make restrictive assumptions about the data - i.e. nonlinearity, non-stationarity. We believe topological data analysis (TDA) can be of benefit in these situations. The process of delay coordinate reconstruction ``unfolds” a scalar time-series into a point cloud in Rm. We can then compute the persistent homology of the reconstructed data to obtain a topological signature. With the ultimate goal of regime shift detection in mind, we choose to use the witness complex - a sparse simplicial complex - for these computations. Topologically accurate delay reconstruction requires appropriate choices for the dimension m and time delay. We introduce novel witness relations that incorporate time and improve the robustness of the resulting homology with respect to choice of delay. The new relations seek to inhibit data points from witnessing landmarks traveling in dissimilar directions, as these can create false connections. We explore how these relations can ameliorate additional challenges that arise when dealing with nonuniform samples of strange attractors. Witness Complexes for Time Series Analysis
Dec. 06, 2017 4:03pm (MATH 3…	Grad Student Seminar Ruofan Li X Chebyshev polynomials (of the first kind) are one of the simplest family of maps that appear in the study of dynamical system. They can also be found in many branches of mathematics: complex analysis, differential equation, number theory and etc.. This talk will cover the definition of Chebyshev polynomials and some basic properties of them. Introduction to Chebyshev polynomials
Dec. 06, 2017 5pm (Math 350)	MathClub Faan Tone Liu (CU Boulder) X In this meeting, we will learn how to fold two particular units in modular origami. We will use some basic geometry theorems to calculate the angles within the units, and then construct a cube and a dodecahedron from the folded units. As time permits we will look at other Platonic and Archimedean solids and investigate how they might be constructed from modular origami units. Solids, Geometry and Folding
Dec. 07, 2017 12:10pm (MATH …	Kempner Geoffrey Grimmett (Cambridge) X The problem of self-avoiding walks (SAWs) arose in statistical mechanics in the 1940s, and has connections to probability, combinatorics, and the geometry of groups. The basic question is to count SAWs. The so-called 'connective constant' is the exponential growth rate of the number of n-step SAWs. We summarise recent joint work with Zhongyang Li concerned with the question of how the connective constant depends on the choice of graph. This work includes equalities and inequalities for connective constants, and a partial answer to the so-called 'locality problem' for graphs and particularly Cayley graphs. Self-avoiding walks on graphs and groups
Dec. 07, 2017 3pm (MATH 350)	Probability Manuel Lladser (Applied Math, CU Boulder) X In this talk, I will present work in progress to approximate the distribution of so-called linear functionals of paths in Markov chains. Archetypical examples of these are sojourn-times, such as those encountered in genomic sequence analyses, telecommunication protocols, and inventory models. Approximating the distribution of linear functionals is a challenging problem in transient regimes because exact computations, as well as stationarity assumptions, are typically infeasible in such regimes. Instead, using low-rank operators and probabilistic arguments, we will see how to approximate the distribution of these functionals in total variation distance - provided the existence of a so-called “regeneration” set; in particular, this setting encompasses Harris-recurrent Markov chains. This work is in collaboration with Dr. Barrera from Universidad Adolfo Ibañez in Chile. Non-asymptotic approximation of Markovian functionals in transient regimes
Dec. 12, 2017 10am (Math 350)	Functional Analysis Jonathan Brown (University of Dayton) X Let $G$ be an étale groupoid. In joint work with Nagy, Reznikoff, Sims and Williams, we study a subgroupoid $G'$ of $G$ consisting of isotropy, in an effort to determine when a representation of $C(G)$ is injective. We show that a representation is injective on $C(G)$ if and only if its restriction to $C(G )$ is, and that when $G'$ is closed, then $C(G )$ is a Cartan subalgebra of $C(G)$ . Now, Renault in 2008 showed that given a Cartan subalgebra $D$ of a $C^{}$ -algebra $A$ , one can construct a twist $T$ so that $C(T)$ is isomorphic to $A$ . In this talk, I will first describe my joint results with Nagy et al. and then show how the work of Muhly, Renault and Williams can be used to explicitly construct a twist associated to the inclusion of $C(G )$ into $C(G)$ when $G'$ is all of the isotropy. I will then point out how this fails more generally. Canonical Cartan Subalgebras of Étale Groupoid $C^{}$ -Algebras and the Construction of Twists Sponsored by the Meyer Fund
Dec. 12, 2017 12:10pm (MATH …	Kempner Kenneth McLaughlin (CSU) X Some surprising questions in analysis arise in the interconnections of the topics in the title. We will encounter zeros of the Taylor approximants of exp(z), and other analytic functions. We will consider questions of support of equilibrium charge distributions in the plane. Semi-classical analysis of d-bar problems will provide merriment along the way. Random matrices, d-bar problems, and approximation theory

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