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

Events for May – September 2017

Return to this week

May. 02, 2017 10am (MATH 350)	Geometry/Analysis Robert Bryant (Duke University) X A Riemannian manifold $M,g)$ is said to be {\it curvature-homogeneous} if it is homogeneous to second order, i.e., if, for any two points in $M$ the Riemannian curvature tensors are equivalent under some isometry of the two tangent spaces. Of course, a locally homogeneous metric is curvature-homogeneous, but the converse is not true in dimensions greater than $2$ . (For a surface (i.e., in dimension $2$ ) curvature-homogeneity is equivalent to having constant Gaussian curvature, and such metrics are, of course, all classified locally and they are locally homogeneous.) Already in dimension $3$ , there are many questions about the existence and generality of curvature homogeneous metrics, even locally. In this case, curvature-homogeneity is equivalent to having the eigenvalues of the Ricci curvature be constant, which is a system of partial differential equations on the metric. In this talk, I will review what is known about such metrics in dimension $3$ , particularly the work of O. Kowalski and his collaborators during the 1990s. I will show that, for certain values of the eigenvalues of the Ricci tensor, these partial differential equations are integrable by the Darboux’ method, which yields some surprising relations with classical subjects, such as the theory of holomorphic curves in the complex projective plane and the geometry of contact curves in the $3$ -sphere. Curvature-homogeneous metrics in dimension 3 Sponsored by the Meyer Fund
May. 02, 2017 11am (MATH 350)	Number Theory Cam Stewart (University of Waterloo) X Let F be a binary form with integer coefficients, non-zero discriminant and degree d with d at least 3.. We shall discuss the problem of estimating the number of square free and more generally k-free integers of absolute value at most Z represented by F. This is joint work with Stanley Xiao. On the representation of k-free integers by binary forns
May. 02, 2017 1pm (MATH 220)	Peter Mayr (CU Boulder) A loop that is not supernilpotent but finitely based
May. 02, 2017 3pm (Math 220)	Functional Analysis Leonard Huang (CU Boulder) X If $f$ is a complex-valued continuous function on the unit circle $𝕋$ that is even (i.e., $f(ei θ) = f(e- i θ)$ for all $θ ∈ R$ ), and all we know about $f$ is its average value on the $n$ -th roots of unity for each $n ∈ N$ , then is it possible to recover $f$ itself from this information? By applying basic Fourier analysis and exploiting properties of the Möbius function and the divisor function, we show that the question has an affirmative answer if $f$ is assumed to be $C2$ on $𝕋$ and to have mean $0$ (i.e., $∫02 π f(ei θ) ~ d/θ = 0$ ). When $f$ is not even, we describe how $f$ may be recovered from the average values of appropriate phase shifts of $f$ on roots of unity. Number-Theoretical Aspects of Averaging a Function on the Unit Circle on Roots of Unity
May. 02, 2017 3pm (Math 350)	Algebraic Geometry Philip Engel (Harvard University) X Philip Engel: The Hurwitz theory of elliptic orbifolds Consider a tiling of a compact, oriented surface by triangles, squares, or hexagons. Enumeration of such tilings can be phrased in the language of Hurwitz theory of an elliptic orbifold. There is a combinatorial curvature associated to each vertex. We will outline a proof that the generating series for the number of tilings with a given number of tiles and specified nonzero curvatures lies in a ring of quasi-modular forms. The asymptotics as the number of tiles goes to infinity allows one to derive formulas for the volumes of strata of cubic, quartic, and sextic differentials---in particular, these volumes are a power of pi times a rational number. This generalizes work of Eskin and Okounkov in the case of abelian and quadratic differentials The Hurwitz theory of elliptic orbifolds Sponsored by the Meyer Fund
May. 03, 2017 4:03pm (MATH 3…	Grad Student Seminar Robert Hines X What do you get when you take something combinatorial (the free group on two generators), cram it any which way into something geometric (SO(3) acting on the sphere), and take for granted the ability to pick apart the resulting mess (the axiom of choice)? Banach-Tarski is what. We'll prove that one can "double the ball," i.e. there is a bijection B\to B\cup B that is defined piecewise by isometries on a finite partition of B. Free bonus "joke" - Q: What's an anagram of "Banach-Tarski"? A: "Banach-Tarski, Banach-Tarski" The Banach-Tarski paradox
May. 04, 2017 3pm (MATH 350)	Probability Yuval Peres (Microsoft Research) X Given $n$ uniform points on the surface of a sphere, how can we partition the sphere fairly among them in an equivariant way? "Fairly" means that each region has the same area. "Equivariant" means that if we rotate the sphere, the solution rotates along with the points. It turns out that if the given points apply a two-dimensional gravity force to the rest of the sphere, then the basins of attraction for the resulting gradient flow yield such a partition—with exactly equal areas, no matter how the points are distributed. Moreover, this partition minimizes, up to a bounded factor, the average distance between points in the same cell. I will also present an application to almost optimal matching of $n$ blue uniform points to $n$ red uniform points on the sphere. This is joint work with Nina Holden and Alex Zhai. Gravitational allocation to uniform points on the Sphere
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

Main menu

Search

Other ways to search:

Events for May – September 2017

Geometry/Analysis

Number Theory

Functional Analysis

Algebraic Geometry

Grad Student Seminar

Probability

Number Theory

Probability

Grad Student Seminar

Init Conditions

Kempner

Lie Theory

Topology

Grad Student Seminar

Init Conditions

Functional Analysis

Lie Theory

Topology

Grad Student Seminar

Init Conditions

Lie Theory

Topology

Grad Student Seminar

Init Conditions

Functional Analysis

Lie Theory

Topology