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Events for June – October 2017

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Jun. 15, 2017 12pm (MATH 350)	Number Theory Elena Fuchs (University of California Davis) X In the early 70’s, the concept of “expander graphs” was introduced as an optimal model for networks of arbitrary size. Back then, it was not even known whether such graphs exist or not. Today, we not only know that they exist, but have seen their importance come up in a great spectrum of fields in mathematics and computer science. In this talk, we will explore what these graphs are and give an idea about how they have recently made a splash on the number theory scene. What network optimization has to do with number theory
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 220)	Agnes Szendrei (CU Boulder) Local term operations on ultrapowers, Part 2
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 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

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