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 April – August 2018

Return to this week

Apr. 03, 2018 11am (MATH 350)	Number Theory Bill Duke (UCLA) X This is joint with Nick Andersen. We introduce some analogues of the Markov spectrum defined in terms of modular billiards and consider the problem of characterizing that part of the spectrum below the lowest limit point. Markov spectra for modular billiards
Apr. 03, 2018 2pm (MATH 350)	Lie Theory Jieru Zhu (Oklahoma) X The hyperoctahedral group is the wreath product between the cyclic group of order 2 and the symmetric group. In 1997, Green defined the hyperoctahedral Schur algebra as the centralizer of the hyperoctahedral group acting on a tensor space. This action commutes with a Levi Lie subalgebra of the general linear Lie algebra, where the two actions fully centralize each other, and the Schur algebra is a quotient of the tensor product of quantum groups. This leads to two presentations of the Schur algebra, and is also true when the cyclic group has higher orders, when the centralizer is called the cyclotomic Schur algebra. One presentation implies a categorification of the cyclotomic Schur algebra, following the categorification of the quantum groups by Khovanov-Lauda-Rouquier. Presenting and categorifying cyclotomic Schur algebras Sponsored by the Meyer Fund
Apr. 03, 2018 3pm (MATH 350)	Algebraic Geometry Dawei Chen (Boston College) X An abelian differential induces a flat metric such that the underlying Riemann surface can be realized as a plane polygon. Varying the shape of such polygons induces a GL(2,R)-action on the moduli space of abelian differentials. The corresponding GL(2,R)-orbit closures are called affine invariant submanifolds, where "affine" refers to the locally linear structure under the period coordinates. In this talk we explore the amusing question whether affine invariant submanifolds are affine varieties in the sense of algebraic geometry. Are affine invariant submanifolds affine? Sponsored by the Meyer Fund
Apr. 03, 2018 4pm (MATH 220)	Topology Katharine Adamyk (CU Boulder) X Abstract: In this talk, we will consider stable model categories (under some conditions) with a set of compact generators. A theorem of Schwede and Shipley describes an equivalence between the homotopy categories of such a model category and the endomorphism category of the set of generators. In particular, we will see that an equivalence can be given by replacing the model category with an appropriate category of symmetric spectra. Some familiarity with model categories and their homotopy categories will be assumed, but there will be a brief overview of these topics, as well as an introduction to symmetric spectra. Classification of Stable Model Categories
Apr. 03, 2018 4pm (MATH 350)	Algebraic Geometry Matt Grimes (Boston College) X Title: Contracting the Weierstrass locus with variation of GIT Abstract: A fundamental problem in the study of moduli spaces is constructing quotient spaces under a group action. The solution of Geometric Invariant Theory is to select a subspace for which the group action is well-behaved. In general, there can be many such subspaces, which leads to variation of GIT. The goal of the talk is to discuss recent work in which VGIT allows us to construct several related moduli spaces of marked genus two curves. Along the way, we will emphasize accessibility and background by discussing the ideas behind GIT as well as important examples. Contracting the Weierstrass locus with variation of GIT Sponsored by the Meyer Fund
Apr. 04, 2018 4:03pm (MATH 3…	Grad Student Seminar Noah Williams X Have you ever had difficulty factoring large degree polynomials? Come to this week's Slow Pitch, where we will discuss how adding a little randomness might help. More specifically, we will explore the concept of "central tendency" as it relates to locating the roots and critical points of certain classes of random polynomials over \mathbb{C}. Hopefully, you'll learn about some standard probability tools, and get a flavor of what I'm working on with Dr. O'Rourke. This talk is intended to be accessible to all math grad students; suggested prerequisites are a solid understanding of Calculus I including derivatives, integrals, and the knowledge that imaginary numbers exist on another plane. Random Points on Random Polynomials
Apr. 04, 2018 5pm (Math 350)	MathClub Agnes Beaudry (CU Boulder) X In this talk I will describe how algebraic topologists associate algebraic objects to geometric shapes in order to study their properties using the powerful tools of algebra. I will explain how some of these tools are now being used to study large data sets. Our guest star, CU graduate student Nikki Sanderson, will explain an example that appears in her research. Transforming shapes into algebra
Apr. 05, 2018 3pm (MATH 350)	Probability Philip Matchett Wood (University of Wisconsin-Madison) X A non-backtracking random walk on a graph is a directed walk with the constraint that the last edge crossed may not be immediately crossed again in the opposite direction. This talk will give a precise description of the eigenvalues of the transition matrix for the non-backtracking random walk when the underlying graph is an Erdos-Renyi random graph on n vertices, where edges present independently with probability p. We allow p to be constant or decreasing with n, so long as p*sqrt(n) tends to infinity. The key ideas in the proof are partial derandomization, applying the Tao-Vu Replacement Principle in a novel context, and showing that partial derandomization may be interpreted as a perturbation, allowing one to apply the Bauer-Fike Theorem. Joint work with Ke Wang at HKUST (Hong Kong University of Science and Technology). Limiting eigenvalue distribution for the non-backtracking matrix of an Erdos-Renyi random graph
Apr. 10, 2018 11am (MATH 350)	Number Theory Vesselin Dimitrov (IAS (Princeton)) X Consider a pair $X,L)$ of a regular and projective algebraic variety over $ℚ$ and a semipositive adelically metrized line bundle $\hat{L}$ over $X$ . Assume that all of Zhang's successive minima of the pair $X,L)$ are equal, or equivalently, that the infimum of the associated height function $hL : X(Q) → R$ is reached by some Zariski-generic sequence. In that setting, I will overview some recent progress on the following question: To what extent does the Galois equidistribution of the small points of $X,L)$ persist when the test function has a logarithmic singularity along some Zariski-closed subset $Z$ of $X$ ? At its core this is a Diophantine approximation problem for arithmetically small points and the fixed algebraic target set $Z$ . The answer turns out to be affirmative if and only if all components of the singular set Z are either divisors of minimum height (Chambert-Loir and Thuillier), or algebraic cycles of codimension at least 2 in $X$ . The main Diophantine approximation result, in its most fundamental case where the ambient arithmetic variety is a linear algebraic torus $\matbb{G}_m^d$ and the approximants are torsion points, has applications to homological torsion asymptotics in the congruence layers of infinite solvable covers of a manifold. A spinoff of the involved technique also leads to the intersection stability property of the finite unions of minimum height subvarieties of $X,L)$ , giving a new approach for the Bogomolov conjecture that applies over both number fields as well as function fields of arbitrary characteristic. Lastly, and time permitting, I will describe an approach to the analogous Diophantine approximation problem in the Shimura setting, when all components of the target set have codimension 2 or higher. Part of this work is joint work with Philipp Habegger. Diophantine approximation with special and arithmetically small points
CANCELED Apr. 10, 2018	Kempner Robert S. Maier (University of Arizona) TBA
Apr. 10, 2018 3pm (MATH 350)	Topology Daniel Berwick-Evans (UIUC) X Modular forms appear in a wide variety of contexts in physics and mathematics. For example, they arise in two dimensional quantum field theories as certain observables. In algebraic topology, they emerge in the study of invariants called elliptic cohomology theories. A long-standing conjecture suggests that these two appearances of modular forms are intimately related. After explaining the ingredients, I’ll describe some recent progress. Modular forms, physics, and topology
Apr. 11, 2018 4:03pm (Math 3…	Grad Student Seminar MIchael Wheeler X Ultrafilters are typically described and used as highly abstract set theoretic objects that just happen to have several very nice properties. This talk will arrive at the definition of an ultrafilter by analyzing what types of voting systems have certain nice properties. We will then use the intuition that ultrafilters are "good" voting systems to describe ultralimits and ultraproducts as the results of voting in particular contexts. No prior knowledge of ultrafilters or their many amazing uses will be assumed. Using Ultrafilters to Vote in an Infinite World
Apr. 12, 2018 2pm (Math 350)	Functional Analysis Paul Muhly (University of Iowa) X In this talk, which is based upon joint work with Erin Griesenauer and Baruch Solel, I will discuss advances in the problem of identifying Arveson’s boundary representations and $C^{}$ -envelopes of homogeneous $C^{}$ -algebras built from algebras of generic matrices. These algebras, in turn, may be viewed as cross sections of certain holomorphic matrix bundles that arise naturally when one tries to view the free algebra on some number of generators in terms of matrix-valued functions on its space of finite-dimensional representations. Holomorphic Matrix Bundles: A Natural Setting for Free Theory Sponsored by the Meyer Fund
Apr. 17, 2018 12:10pm (MATH …	Kempner Petr Vojtechovsky (University of Denver) X We present three case studies of enumeration in nonassociative algebra: quandles, code loops, and Bruck loops. Quandles are algebraic structures designed to color arcs of oriented knots and they also form a well-studied class of set-theoretical solutions of the Yang-Baxter equation. Their classification is based on a representation in symmetric groups and we extend existing results by several orders of magnitude in complexity. Code loops first appeared in Conway's construction of the Monster group and the general case was introduced by Griess. Their classification is based on trilinear alternating forms, and we again significantly improve upon existing results. Finally, Bruck loops provide framework for Einstein's relativistic addition of vectors and we use central extensions to count Bruck loops of small odd prime power orders. All three results require extensive computer calculations. This is joint work with Seung Yeop Yang, Eamonn O'Brien and Izabella Stuhl, in order of appearance. Enumeration in nonassociative algebra
Apr. 17, 2018 1pm (MATH 220)	Petr Vojtechovsky (University of Denver) X We give more details on the colloquium talk. Isomorphism problems for Latin squares
Apr. 17, 2018 2pm (MATH 350)	Lie Theory Niamh Farrell (Kaiserslautern) X In joint work with Radha Kessar, we show that the Morita Frobenius numbers of the $p$ -blocks of quasi-simple finite groups are less than or equal to four, and hence the basic algebras of such $p$ -blocks are defined over the finite field of $p4$ elements. I will explain the connection between this result and Donovan's Conjecture and illustrate how recent results of Bonnafè—Dat—Rouquier played a crucial role in our methods. Rationality of blocks of quasi-simple finite groups Sponsored by the Meyer Fund
Apr. 17, 2018 3pm (MATH 350)	Topology Markus Pflaum (CU Boulder) Hochschild Homology and Cyclic Homology of Convolution Algebras
Apr. 18, 2018 5pm (Math 350)	MathClub Divya Vernerey (CU Boulder) X Viscous fingering is the formation of finger-like patterns due to instability in the interface between two fluids in a porous media. Starting with the Navier-Stokes equations (which describes the motion of viscous fluids), I will derive the simplified Darcy’s law. One application of Darcy's law is to analyze oil and gas recovery from traditional and modern fracking techniques. I will then conclude with an experiment where viscous fingering can be seen: the Hele-Shaw cell. Viscous Fingering
Apr. 19, 2018 2pm (MATH 350)	Functional Analysis Robin Deeley (CU Boulder) X I will speak about joint work in progress with Ian Putnam and Karen Strung. The goal of the project is to study the existence of minimal dynamical systems and, more generally, minimal equivalence relations. In particular, I will discuss the following question: Given a compact Hausdorff space, does there exist a minimal homeomorphism on it? Although the answer is no, a similar question has a positive answer for a finite CW-complex. This question, and the question of which $C^{}$ -algebras can be realized as groupoid $C^{}$ -algebras, are the motivation for our constructions. Minimal Dynamical Systems and Groupoids with Prescribed $K$ -Theory
Apr. 19, 2018 3pm (MATH 350)	Probability Manuela Girotti (CSU) X We study the distribution of the smallest singular eigenvalues for the finite product of certain random matrix ensemble, in the limit where the size of the matrices becomes large. The limiting distributions that we will study can be expressed as Fredholm determinants of certain integral operators, and generalize in a natural way the extensively studied hard edge Bessel kernel determinant. We will express such quantities in terms of a 2x2 Riemann-Hilbert problem, and use this representation to obtain so-called large gap asymptotics. This is a joint work with Tom Claeys (UC Louvain, Belgium) and Dries Stivigny (KU Leuven, Belgium). Smallest singular value distribution and large gap asymptotics for products of random matrices
Apr. 24, 2018 11am (MATH 350)	Number Theory Comp exam scheduled No seminar today
Apr. 24, 2018 12:10pm (MATH …	Kempner Robert S. Maier (University of Arizona) X The most familiar special functions are hypergeometric functions, which appear in many areas of mathematics. They include the Legendre functions, which arise in harmonic and numerical analysis, and elliptic integrals. All these functions have one or more free parameters, and the parameter values for which they can be expressed in closed form (e.g., because they become algebraic, with finite monodromy) have in many cases been characterized: for the original Gauss function, by Schwarz and Klein; for generalizations, by Beukers and Heckman in the 1980s. But there is a shortage of algorithms for constructing explicit closed-form expressions, and even of transformation formulas that relate such functions to ones with different parameter values. In this talk, I sketch recent results: (i) algebraic-geometric uniformizations of certain generalized hypergeometric functions, (ii) transformation formulas for elliptic integrals, extending ones found by Ramanujan, and (iii) Lie-theoretic recurrences satisfied by the octahedral Legendre functions. Explicit formulas for hypergeometric and Legendre functions
Apr. 24, 2018 1pm (MATH 220)	Trevor Jack (CU Boulder) X We introduce a method of investigating semigroup properties using graph theory. Given a transformation semigroup generated by transformations $a1,...,ak$ on n letters, we produce a graph with $n^{d}$ vertices and directed edges corresponding to the generators acting on the vertices component-wise. The number of components, d, depends upon which semigroup property we are investigating. We will sketch several results obtained thus far, including: (a) whether a semigroup is nilpotent, (b) whether a semigroup is a band, and (c) whether a semigroup satisfies a given equation $φ(x1,...,xm) = ψ(x1,...,xm)$ . Investigating semigroup properties using graphs
Apr. 24, 2018 2pm (MATH 350)	Lie Theory Henry Kvinge (CSU) X For a given tower of algebras the associated Heisenberg category captures the combinatorial structure of induction/restriction functors between these algebras via a graphical calculus of string diagrams. It can also be shown that the center of this category (the closed diagrams) controls the centers of all algebras in the tower simultaneously. In this talk we will discuss examples of this phenomenon, focusing on the case where the tower of algebras is either group algebras of symmetric groups or the Sergeev superalgebras. We will show how known (inhomogeneous) bases of the symmetric functions appear naturally from the diagrammatics in each case, and explore properties of these symmetric functions diagrammatically. Finally, we will discuss a surprising connection to Markov processes on branching graphs for these towers of algebras. Symmetric functions, towers of algebras, and centers of Heisenberg categories
Apr. 24, 2018 3pm (MATH 350)	Topology Paul Lessard (CU Boulder) X Week 1 of an Algebraic Topology Course from Another World In this talk we will describe the homotopy category of the category of spaces as the localization of \Cat at the smallest class of morphisms which is weakly saturated and can be said to know that: - cones are trivial - Quillen's theorem A holds. From this description of the category of spaces we will unify all the ways in which categories of presheaves, e.g.: simplicial sets, cubical sets, globular sets, etc. model spaces by way of the universal property of the Yoneda embedding. Quillen's Theorem A and Grothendieck's Asphericite
Apr. 25, 2018 4:03pm (MATH 3…	Grad Student Seminar Sebastian Bozlee X Algebraic geometry teaches us that associated to each commutative ring with unit A is a space, Spec A. Given any A-module M and any element m of M we can associate a subspace of Spec A called the support of m. In other words, it makes sense to ask where module elements live. We will start with a description of Spec A and its closed subschemes, then define support. Time permitting, we will consider examples from polynomials, linear homogeneous differential equations, and linear homogeneous recurrence relations. Where does my module live?
Apr. 26, 2018 1pm (MATH 350)	Topology Xiang Tang (Washington University, St. Louis) X For a compact Lie group action on a smooth manifold, we will introduce a complex of basic relative forms on the inertia space, which was originally constructed by Brylinski. We will explain how basic relative forms can be used to study the Hochschild homology of the convolution algebra. This is work in progress with Markus Pflaum and Hessel Posthuma. Hochschild Homology of Proper Lie Groupoids Sponsored by the Meyer Fund
Apr. 26, 2018 2pm (MATH 350)	Topology Jordan Watts X Fix an irrational number A, and consider the action of the group of pairs of integers on the real line defined as follows: the pair (m,n) sends a point x to x + m + nA. The orbits of this action are dense, and so the quotient topology on the orbit space is trivial. Any reasonable notion of smooth function on the orbit space is constant. However, the orbit space is a group: the orbits of the action are cosets of a normal subgroup. Can we give the space any type of useful "smooth" group structure? The answer is "yes": its natural diffeological group structure. It turns out this is not just some pathological example. Known in the literature as the irrational torus, as well as the infra-circle, this diffeological group is diffeomorphic to the quotient of the torus by the irrational Kronecker flow, it has a Lie algebra equal to the real line, and given two irrational numbers A and B, the resulting irrational tori are diffeomorphic if and only if there is a fractional linear transformation with integer coefficients relating A and B, and so it is of interest in many fields of mathematics. Moreover, it shows up in geometric quantisation and the integration of certain Lie algebroids as the structure group of certain principal bundles, the main topic of this talk. We will perform Milnor's construction in the realm of diffeology to obtain a diffeological classifying space for a diffeological group G, such as the irrational torus. After mentioning a few hoped-for properties, we then construct a connection 1-form on the G-bundle EG --> BG, which will naturally pull back to a connection 1-form on sufficiently nice principal G-bundles. We then look at what this can tell us about irrational torus bundles. Classifying Spaces of Diffeological Groups Sponsored by the Meyer Fund
Apr. 26, 2018 3pm (MATH 350)	Probability Leonard Huang (CU Boulder) X This talk is inspired by the following problem, which has appeared in real-analysis exams at several universities around the world: Let $(xn)n ∈ N$ be a sequence in $ℝ$ . If $n → ∞ (2 xn + 1 - xn) = x$ for some $x ∈ R$ , then prove that $n → ∞ xn = x$ also. One may now ask: Is this result still true if we replace $ℝ$ by some other topological vector space? In this talk, we will prove that the result is true for a wide class of topological vector spaces that includes all locally-convex topological vector spaces, as well as some non-locally-convex ones, such as the $L^{p}$ -spaces for $p ∈ (0,1)$ . We will also construct, using probability theory, an example of a topological vector space for which the result is false. Generalization of a Real-Analysis Exam Problem to a Class of Topological Vector Spaces
May. 01, 2018 11am (MATH 350)	Number Theory Number Theorists of Boulder X Hanson will speak today. Number Theory Lab Meeting
May. 01, 2018 3pm (MATH 350)	Topology Jonathan Belcher (CU Boulder) X The connection between Hochschild and cyclic cohomologies with generalized De Rham homology and index theories for arbitrary algebras has long been established by the work of Connes, Karoubi, Loday, Feigin, Tsygan, et al. Here we generalize these cohomology theories even further, essentially creating a theory that establishes a step-wise bridge between the two. This theory can then be used to establish similar geometric result for manifolds with boundaries and may have applications in exterior differential systems, as well as extend to higher K-theories. On Hochschild and cyclic cohomology
May. 01, 2018 4pm (MATH 350)	Algebraic Geometry Maksym Fedorchuk (Boston College) X Title: Invariant-theoretic Mather-Yau theorem, and applications Abstract: The famous Mather-Yau theorem says that two isolated hypersurface singularities of the same embedding dimension are biholomorphically equivalent if and only if their moduli algebras are isomorphic. Thus determining whether two given moduli algebras are isomorphic becomes an important problem. In the case of quasi-homogeneous hypersurface singularities, Eastwood and Isaev proposed a purely algebraic approach to this problem, rooted in classical invariant theory. For homogeneous singularities, this approach leads to the associated form morphism that assigns to a singularity the Macaulay inverse system of its moduli algebra. The associated form morphism has several marvelous properties, two of which I will discuss in this talk. In joint work with Isaev, we have shown that the associated form morphism preserves GIT polystability (arXiv:1703.00438). This leads to a purely algebraic invariant-theoretic Mather-Yau theorem for homogeneous hypersurface singularities, and to interesting new compactifications of the moduli space of smooth hypersurfaces. The associated form morphism also detects whether a homogeneous polynomial with a non-vanishing discriminant is a direct sum (of Sebastiani-Thom type), and so leads to an algorithm for finding direct sum decompositions over the rationals (arXiv:1705.03452). Invariant-theoretic Mather-Yau theorem, and applications Sponsored by the Meyer Fund
May. 03, 2018 11am (MATH 350)	Geometry/Analysis Zachary Grey (University of Colorado, Boulder, Aerospace Engineering) A Riemmanian View on Active Subspaces: Active Manifold-Geodesics Sponsored by the Meyer Fund
May. 03, 2018 11am (Math220)	Michael Fried (UC Irvine, visiting U Colorado) X I will give an example of a moduli space of curves that looks like it should be connected, but it has two components. Those components will be recognized by a $l i f t$ $i n v a r i a n t$ developed by Fried and Serre. We use this example to illustrate much theory about these spaces, including understanding them as covers of the $j$ -line: their degrees as covers, their genuses, and whether they have fine moduli. An efficient device for making this computation is the sh(ift)-incidence matrix. I will explain this using a 2-page handout. This is a prelude to seeing the relation between this lift invariant and the $W e i l$ $p a i r i n g$ . For a curve $C$ rather than an abelian variety, this is a perfect pairing $H1(C, Zℓ)× H1(C, Zℓ) ↦ H2(C, Zℓ)$ . This pairing first appeared to explain a phenomena on modular curves. This talk is a prelude to showing the Weil pairing in this famous place gets incorporated into this theory, making it available for generalization beyond any previous use of it. Components of Moduli spaces and the Weil Pairing
May. 03, 2018 2pm (MATH 350)	Functional Analysis Kathy Merrill (Colorado College) X Conventional wavelets in two dimensions use the operations of integer translation and dilation by an expansive integer matrix to compress images for more efficient storage and transmission. This talk will discuss wavelets built by replacing the group of integer translations by one of the 17 wallpaper symmetry groups. We will focus on wavelet sets, which can be used to decompose the wavelet representation into irreducibles. Wavelet Sets for Crystallographic Groups
May. 03, 2018 3pm (MATH 350)	Probability Kyle Luh (Harvard) X Despite recent advances in the graph isomorphism problem, the current algorithms still only run in quasipolynomial time. It is known, however, that for graphs with adjacency matrices that have simple spectrum (meaning no repeated eigenvalues) there is a polynomial-time algorithm. The natural question is whether the majority of graphs and matrices fall in this category. It was conjectured by Babai that Erd\H{o}s-R\enyi random graphs with edge probability 1/2 have simple spectrum with high-probability. This conjecture was recently verified by Tao and Vu for all constant p. We extend their result to allow p to depend on the number of vertices (p \geq n^{-1+\delta} for any \delta>0). In particular, we show that a large class of sparse random matrices have simple spectrum with high probability. Along with the proof of this result, we will survey several recurring tools from random matrix theory. This talk is based on joint work with Van Vu. Sparse Random Matrices have Simple Spectrum
May. 08, 2018 11am (MATH 350)	Number Theory Sukumar Das Adhikari (Harish-Chandra Research Institute (Allahabad, India)) X A particular weighted generalization of some classical zero-sum constants was first considered about ten years back. Since then, many people got interested in this generalization. Similar generalizations of other zero-sum constants were also considered and these gave rise to several conjectures and questions; some of these conjectures have been established, some of the questions have been answered. And most interestingly, some applications of this weighted generalization have also been found. After a short discussion on the classical results, we shall have a glimpse of these weighted generalizations. Weighted zero-sum constants: a survey
May. 08, 2018 3pm (MATH 350)	Topology Josh Grochow (CU Boulder) X The Unique Games Conjecture states that approximating certain optimization problems to within some factor is NP-hard; over the past ~15 years it has been one of the most actively researched conjectures in computational complexity. In this talk I will give background on this conjecture, and explain how it is "really" about computational topology. In particular, we can rephrase the Unique Games Conjecture as a certain conjecture on the following computational problem: given given a finite graph Gamma, a finite group G, and a (not-necessarily-principle) G-bundle on Gamma, find the largest subset of Gamma over which the bundle admits a section. This observation originally goes back to Linial (2005), but here we extend it to show that several other aspects of this conjecture are essentially topological in nature. We use this viewpoint to mostly settle an open question of Chen & Freedman (2010). No background in computer science will be assumed. Our hope is that our observations on the topological nature of the Unique Games Conjecture will lead to applications of algebraic topology to the Unique Games Conjecture in the future. Based on joint work with Jamie Tucker-Foltz arXiv:1803.06800, to appear in the 34th International Symposium on Computational Geometry (SoCG 2018). Computational Topology & The Unique Games Conjecture
May. 09, 2018 11am (Math350)	Michael D. Fried (UC Irvine, visiting U Colorado) X Here is one way to say Serre's $O$ (pen) $I$ (mage) $T$ (heorem). Consider the system of modular curve covers $X0,ℓ$ defined as the projective system of spaces $X0(ℓk+1)→ P1j, k≥ 0$ , for an odd prime $ℓ$ . This has a projective system of arithmetic and geometric monodromy groups which are known to be $GL2( Z/ℓk+1)/$ and $SL2( Z/ℓk+1)/$ , $k≥ 0$ , respectively. Then, the $OIT$ intersects the decomposition group of a projective system of points lying over an algebraic value of $j$ with the projective limit of the geometric monodromy groups of $X0,ℓ$ . The $OIT$ says there are just two types of groups depending on which $j$ you choose, called CM and GL $_{2}$ . Modular Towers gives another way to look at this same system, and thereby a road to generalizing it. We look at a mysterious aspect that arises early in Serre's result, the use of the Weil Pairing, and see how that interprets in a new system. Comparing Serre's Open Image Theorem with a new system of Moduli spaces
May. 10, 2018 3pm (MATH 350)	Probability Stanislav Volkov (Centre for Mathematical Sciences, Lund University, Sweden) X Consider a graph G with a subset of "sick" vertices called "the border". A particle released from the origin performs a random walk on G until it comes in the direct contact with a sick particle, at which point it becomes sick itself, and stops walking, thus increasing "the sick border" by one point. A new particle is then released from the origin, and the process repeats, until the origin itself becomes a part of the border. We are interested in the total number xi of particles to be released by this final moment. Incidentally, this model, inspired by personal communications with Yuval Peres (Microsoft), can be viewed as a generalization of the OK Corral model considered previously by Sir John Kingman and myself. (Based on the joint work with Debleena Thacker, Uppsala). Border aggregation model
May. 17, 2018 3pm (MATH 350)	Functional Analysis Kathy Merrill (Colorado College) X This is the second half of the following talk: Conventional wavelets in two dimensions use the operations of integer translation and dilation by an expansive integer matrix to compress images for more efficient storage and transmission. This talk will discuss wavelets built by replacing the group of integer translations by one of the 17 wallpaper symmetry groups. We will focus on wavelet sets, which can be used to decompose the wavelet representation into irreducibles. Wavelet sets for crystallographic groups , part (ii)
May. 18, 2018 3pm (MATH 350)	Functional Analysis Keith Taylor (Dalhousie University) Projections in $L1(G)$
Jun. 26, 2018 2pm (MATH 350)	Lie Theory Kento Nakada (Okayama University) X D. Peterson introduced the notion of "minuscule elements" in Weyl groups. This is a generalization of Grassmannian permutations in symmetric groups. This talk introduces minuscule elements, generalized Young diagrams, and their hook formulae. These are generalizations of the ordinary hook formula for Young diagrams. A hook formula for minuscule elements in Weyl groups
Jun. 26, 2018 3pm (MATH 350)	Lie Theory Manabu HAGIWARA (Chiba University) X Insertions and deletions are operations in a model of synchronization errors in coding theory. This talk introduces relations between such operations and mathematics, in particular, minuscule objects of Weyl groups and combinatorics. Algebraic and Combinatorial Aspects of Insertion/Deletion Operations
Jul. 17, 2018 10am (MATH 350)	Geometry/Analysis Peter Vassiliou (Australian National University) X Control systems, typically nonlinear, abound in our daily experience of the world. Mathematically, they can be described by differential equations endowed with functional parameters. The prototypical example is balancing a broomstick on the tip of your finger. A basic problem in control theory is the following. Suppose a control system $\bsy{\o}$ is in state $A$ and you want to ``steer" it to state $B$ . How do you choose the (functional) parameters in the system -- the controls -- in order to achieve this? One oft-used technique is to find a special type of transformation, $T$ , that maps $\bsy{\o}$ to a certain type of universal linear control system called a Brunovsky normal form, $\bsy{\b}$. The trajectories of $\bsy{\b}$ can easily be written down in terms of arbitrary functions of time and their time derivatives after which $T-1$ maps the trajectories of $\bsy{\b}$ to those of $\bsy{\o}$, from which the steering problem can be solved. If we can construct such a solution, $s$ of $\o$, we will say that it is {\em explicitly integrable}. This settles the steering problem for linearizable control systems which form a small subset of control systems of interest. But while every linearizable system is explicitly integrable, the converse is false and for the past few decades there has been a research program underway to characterize the phenomenon of explicit integrability beyond the linearizable case. However it turns out that the Brunovsky normal forms are familiar objects in differential geometry. They correspond to the contact systems on a special class of jet spaces over the real line. In this talk we will explore this geometry to show how to establish explicit integrability for control systems which are intrinsically nonlinear - those that have no linearizing diffeomorphisms. A key ingredient is the invariance of $\bsy{\o}$ under the free and regular action of a Lie group. Symmetry and Geometric Control Theory Sponsored by the Meyer Fund
Jul. 19, 2018 10am (MATH 350)	Geometry/Analysis Peter Vassiliou (Australian National University) X In previous centuries mathematicians sought solutions of differential equations in formula as a matter of course. This approach to the study of differential systems has fallen out of fashion (and possibly favor) as a result of the vast revolutions in analysis and the types of problems requiring solution in the current epoch. Nevertheless a tremendous heritage in this area has been bequeathed to us by previous generations which we have begun to explore only in the last 4 decades or so. This resurgence has produced a fascinating body of mathematics and its applications, such solitons, Poisson geometry, infinite dimensional hamiltonian systems, Backlund transformations; to name a few. One such 19th century topic, Darboux integrability, has been the subject of a number of recent studies which reveal it to have strong geometric content and utility for constructing explicit solutions in formula of certain partial differential equations. However, because Darboux integrability is a comparatively rare phenomenon it is natural to ask if some weaker form of it may exist so as to be of wider applicability while retaining some useful aspects of the original. In this talk I will briefly recall the basic ideas of this form of integrability and then propose a weaked version which will be explored via a few elementary examples. Time permitting we will also explore its application to certain harmonic maps. Hyperbolic Reduction of Partial Differential Equations Sponsored by the Meyer Fund

Main menu

Search

Other ways to search:

Events for April – August 2018

Number Theory

Lie Theory

Algebraic Geometry

Topology

Algebraic Geometry

Grad Student Seminar

MathClub

Probability

Number Theory

Kempner

Topology

Grad Student Seminar

Functional Analysis

Kempner

Lie Theory

Topology

MathClub

Functional Analysis

Probability

Number Theory

Kempner

Lie Theory

Topology

Grad Student Seminar

Topology

Topology

Probability

Number Theory

Topology

Algebraic Geometry

Geometry/Analysis

Functional Analysis

Probability

Number Theory

Topology

Probability

Functional Analysis

Functional Analysis

Lie Theory

Lie Theory

Geometry/Analysis

Geometry/Analysis