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Events for May – September 2018

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Sep. 27, 2018 5pm (Math 350)	Cat Wilson, Carly Matson, & Krisztina Dearborn X Cat Wilson, Graduate Student Career Development Advisor from Career Services, will join us to briefly introduce herself. Afterwards, there will be an informal workshop on application materials (CV, resume, website, etc). Note: Cat will not stay for this part of the seminar. Use this time to seek feedback from peers. We will share tips, templates, and discuss any other relevant topics. Cat Wilson introduction and workshop on application materials
Sep. 20, 2018 5pm (Math 350)	Carly Matson & Krisztina Dearborn X Brief overviews of suggested timelines for preparing for a career in academia or in industry will be given and a variety of resources will be shared. An informal Q&A about the hiring process in academia will be held with Dr. Robin Deeley. Timeline for preparing for a career while in graduate school
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 (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 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 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
Sep. 04, 2018 10am (MATH 350)	Geometry/Analysis Chi Hin Chan (National Chiao Tung University, Taiwan) X In this talk, we will talk about a recent work, in which we establish the existence of a stationary linear-Stokes flow in an exterior domain of a hyperbolic plane. We assume the no-slip boundary condition and the finite Dirichlet norm condition. Thus, we give the antithesis of the Stokes paradox in the hyperbolic setting. We will indicate why our method also leads to a nontrivial Navier-Stokes flow in an exterior domain of the hyperbolic plane under the same condition. This is a joint work with Magdalena Czubak. About the antithesis of the Stokes Paradox on the hyperbolic plane Sponsored by the Meyer Fund
Sep. 04, 2018 11am (MATH 350)	Number Theory Hanson Smith (CU Boulder) X The talk will be concerned with motivating and presenting the following result: Consider an elliptic curve $E$ over a number field $K$ and let $𝔭$ be a prime of $𝒪_{K}$ lying above a prime $p$ of $ℤ$ . Suppose $E$ has supersingular reduction at $𝔭$ . Fix a positive integer $n$ and define $L$ to be a minimal extension of $K$ such that $E(L)$ has a point of exact order $p^{n}$ . If $𝔭$ is unramified over $p$ , then $L/K$ is an extension of degree $p2n-p2n-2$ that is totally ramified over $𝔭$ . If $𝔭$ is ramified over $p$ , then $(pn)$ still properly divides $L:Q]$ . Using the stronger bound, one can show that sporadic points on the modular curve $X1(pn)$ cannot correspond to elliptic curves that are supersingular at $𝔭$ with $𝔭$ unramified over $p$ . These methods generalize to $X1(N)$ with $N$ composite. Ramification in the Division Fields of Elliptic Curves and an Application to Sporadic Points on Modular Curves
Sep. 04, 2018 1pm (MATH 350)	Ulam D. Kaledin X Enhanced, or infty-categories are proving to be a useful working tool in many areas of homological algebra, but their definitions in current use are quite cumbersome and depend on hardcoded arbitrary choices. I will try to give a brief overview of the area, explain why it is indeed useful for real-life mathematics, and then present a somewhat more invariant approach to the subject based on Grothendieck's idea of a "derivator". On the notion of an enhanced category
Sep. 04, 2018 3pm (Math 350)	Algebraic Geometry David Holmes (University of Leiden) X It is well-known that the Abel-Jacobi map does not extend over the boundary of the moduli space of stable marked curves. We approach this problem by making (logarithmic) blowups of the moduli space, constructing a `universal’ resolution of the indeterminacies of the Abel-Jacobi map. After considering some elementary examples, we will show how to apply this construction to the problem of compactifying the double ramification cycle, and show that the resulting compactification is compatible with various conjectures and formulae in the literature. Extending the Abel-Jacobi map Sponsored by the Meyer Fund
Sep. 04, 2018 4pm (MATH 350)	Topology Markus Pflaum (CU Boulder) K-homology
Sep. 05, 2018 4:03pm (MATH 3…	Grad Student Seminar Lucas Gagnon (CU Boulder) X A $q$ -analog of a theorem or formula is a generalization involving a parameter $q$ so that $q → 1$ gives the original result. The $q$ -binomial coefficient, or Gaussian binomial coefficient is a well known example, generalizing a large number of the properties of binomial coefficients in surprising and interesting ways. We will motivate this analogy by briefly reviewing the properties of the binomial coefficient, and then define and discuss the $q$ -binomial, touching on topics relating to finite fields, non-commutative geometry, and lattice paths. Time permitting, the talk will end with a fun application of the $q$ -binomial coefficient to the game SET. q-Analogs and the q-Binomial
Sep. 11, 2018 1pm (MATH 350)	Ulam D. Kaledin X This is a continuation of my talk on Sep. 4. although it should be understandable by itself. I will give a precise derivator-style definition of an enhanced category and explain the main points of the theory. On the notion of an enhanced category, II
Sep. 11, 2018 1pm (MATH 220)	Peter Mayr X Constraint Satisfaction Problems (CSP) include a wide variety of classical decision problems, like satisfiability of Boolean formulas, colorability of graphs, solvability of systems of linear equations,... and real-life problems, like scheduling, database queries. The Dichotomy Conjecture by Feder & Vardi states that every CSP is either solvable in polynomial time or NP-complete. It has just been verified independently by Bulatov and by Zhuk using two different algebraic approaches. We give an introduction to CSP, the algebraic formulation of the Dichotomy Conjecture and, time permitting, a broad overview of Zhuk's algorithm. See https://arxiv.org/abs/1704.01914 More details of the solution will be filled in throughout the semester. Constraint Satisfaction Problems
Sep. 11, 2018 2pm (MATH 350)	Lie Theory Nat Thiem (CU) X The character theory of finite groups has numerous basic questions that are often already quite involved: enumerating of irreducible characters, their character formulas, point-wise product decompositions, and restriction/induction between groups. A supercharacter theory is a framework for simplifying the character theory of a finite groups, while ideally not losing all important information. This talk examines one such theory that straddles the gap between retaining valuable group information while reducing the above questions to more combinatorial lattice constructions. Joint with Aliniaeifard. The structure of normal lattice supercharacter theories
Sep. 11, 2018 2pm (MATH 220)	Agnes Szendrei (CU Boulder) X The concept of a Cofinality Spectrum Problem (CfSP) was introduced recently by M. Malliaris and S. Shelah (J. Amer. Math. Soc., 2016), and was used to obtain spectacular results in model theory and set theoretic topology. In model theory the Malliaris-Shelah results on CfSPs shed new light on Keisler’s order -- a notion from the 1960’s to classify first order theories. In set theoretic topology these results were used to prove that the cardinals p and t related to the continuum are equal (in ZFC), although for decades, this equality was expected to be independent of ZFC. Overview of the Malliaris--Shelah paper, Part 1
Sep. 11, 2018 3pm (MATH 220)	Topology Sam Nariman (Northwestern University) Topology Seminar Pretalk Sponsored by the Meyer Fund
Sep. 11, 2018 3pm (MATH 350)	Algebraic Geometry Zheng Zhang (CU Boulder) X The period map is a powerful tool for studying moduli spaces, and has been applied successfully to abelian varieties, K3 surfaces, cubic threefolds/fourfolds, and hyper-Kahler manifolds. However, for some interesting moduli problems (e.g. moduli spaces for pairs of varieties) there might be no obvious way to construct periods. Joint with R. Laza and G. Pearlstein, we construct a period map for cubic pairs consisting of a cubic threefold and a transverse hyperplane using a variation of the construction by Allcock, Carlson and Toledo (which allows us to encode a cubic pair as a “lattice polarized” cubic fourfold). The main result is that the period map induces an isomorphism between a GIT model of the moduli of cubic pairs and the Baily-Borel compactification of some locally symmetric domain. On the moduli space of pairs consisting of a cubic threefold and a hyperplane
Sep. 11, 2018 4pm (MATH 350)	Topology Sam Nariman (Northwestern University) X There are at least three different approaches to construct characteristic invariants of a flat symplectic bundle. Reznikov generalized Chern-Weil theory for finite dimension Lie groups to the infinite dimensional group of symplectomorphisms. He constructed nontrivial invariants of symplectic bundles whose fibers are diffeomorphic to complex projective spaces. Kontsevich used formal symplectic geometry to build interesting classes that are not yet known to be nontrivial. For surface bundles whose holonomy groups preserve the symplectic form, Kotschick and Morita used the flux homomorphism to construct many nontrivial stable classes. In this talk, we introduce infinite loop spaces whose cohomolgy groups describe the stable characteristic invariants of symplectic surface bundles. As an application, we give a homotopy theoretic description of Kotschick and Morita's classes and prove a result about codimension 2 foliations that implies the nontriviality of KM classes. On the moduli space of flat symplectic surface bundles Sponsored by the Meyer Fund
Sep. 12, 2018 4pm (MATH 350)	Grad Student Seminar Leo Herr (CU Boulder) X Schemes and Varieties have a reputation for being somewhat challenging to become familiar with. Is it too late to recall their original geometric intuition? No! We'll see a handful of down-to-earth examples of varieties encoded by cones in, say 3-d real space. Maybe we'll get to resolution of singularities or Stanley's Theorem. Toric Varieties and Convex Geometry
Sep. 13, 2018 11am (Math 220)	SPORT Graduate Internship (NSA) X The SPORT program at the National Security Agency (NSA) offers graduate students the opportunity to apply their academic knowledge in a stimulating professional environment. As a SPORT intern you will work closely with full time Operations Research analysts applying academic and technical skills to challenging, real-world problems. Internships are paid and are 12 weeks in duration (May-August). Applications accepted September 1st through October 31st. Summer Program for Operations Research Technology at NSA
Sep. 18, 2018 10am (MATH 350)	Geometry/Analysis Yuhao Hu (University of Colorado, Boulder) Geometry of Backlund transformations Sponsored by the Meyer Fund
Sep. 18, 2018 1pm (MATH 220)	Peter Mayr X We discuss several classical reductions between CSPs over finite constraint languages. In particular we show that each constraint language may be replaced by the singleton expansion of its core. Further the complexity of CSP(Gamma) is determined by the variety generated by its polymorphism algebra. CSP reductions
Sep. 18, 2018 2pm (MATH 220)	Agnes Szendrei (CU Boulder) Overview of the Malliaris--Shelah paper, Part 2
Sep. 18, 2018 2pm (Math 350)	Lie Theory Julianne Rainbolt (Saint Louis University) X Let $\tilde{G}$ denote a connected reductive algebraic group defined over an algebraically closed field of characteristic $p > 0$ . Let $F : \tilde{G} \to \tilde{G}$ be a Frobenius endomorphism. Let $G$ be the finite group of Lie type which is the fixed points of $F$ . Let $B$ be an $F$ -stable Borel subgroup of $\tilde{G}$ and let $T$ be an $F$ -stable maximal torus of $\tilde{G}$ contained in $B$ . Let $N = NG(T)$ . Denote the Weyl group of $G$ by $W = NF/TF$ . The element $\overset{\cdot}{w}$ will denote a preimage of $w ∈ W$ with respect to the natural surjection from $N^{F}$ to $W$ . The double cosets $B^{F} \overset{\cdot}{w} B^{F}$ are called the Bruhat cells of $G$ . An element $x ∈ G$ is called regular if the dimension of its centralizer is minimal. In this talk, we will discuss necessary and sufficient conditions for Bruhat cells to contain only regular elements. Furthermore, we will investigate Bruhat cells that contain both regular and nonregular elements but have cosets consisting entirely of regular elements. Cosets and Double Cosets Containing only Regular Elements Sponsored by the Meyer Fund
Sep. 19, 2018 4pm (MATH 350)	Grad Student Seminar Andrew Campbell (CU Boulder) X The distribution of eigenvalues of random matrices is a central idea in random matrix theory. Universality is a phenomenon which holds for a wide class of random variables, usually motivated by normal random variables. We will look at Wigner's famous semicircle law, the circular law, the elliptic law, and results on the distributions of eigenvalues on the unit circle for probability measures on compact matrix groups. No prior knowledge on probability or random matrix theory will be assumed. Pictures will be included. Universality, Eigenvalues of Random Matrices, and Circles
Sep. 20, 2018 2pm (MATH 350)	Functional Analysis Robin Deeley (CU Boulder) X I will discuss joint work with Magnus Goffeng and Allan Yashinski on the construction of non-zero projections in certain C-algebras. To begin, the case of continuous trace C-algebras will be discussed. The results in this case lead to a natural conjecture for more general type I C*-algebras. However, as will be outlined via explicit examples, even in the case of Fell algebras the question of the existence of non-zero projections is quite subtle. On the existence of projections in Fell algebras
Sep. 21, 2018 12pm (MATH 350)	Ulam Roman Bezrukavnikov (MIT) X I will review old results (joint with I. Mirkovic and D. Rumynin) on localization theory for representations of semi-simple Lie algebras and then discuss recent results and conjectures extending them to more general contexts, emphasizing relation to derived algebraic geometry. Modular representations and geometry
Sep. 25, 2018 11am (MATH 350)	Number Theory Robert Hines (CU Boulder) X We consider approximation of vectors $z∈ F⊗R≅Rr×Cs$ by elements of a number field $F$ and construct examples of badly approximable vectors. These examples come from compact subspaces of $SL2(OF) SL2(F⊗R)$ naturally associated to (totally indefinite, anisotropic) $F$ -rational binary quadratic and Hermitian forms, a generalization of the well-known fact that quadratic irrationals are badly approximable over $ℚ$ . Examples of badly approximable vectors over number fields
Sep. 25, 2018 1pm (MATH 220)	Peter Mayr X We show that if a constraint language does not have a WNU polymorphism, then its CSP is NP-complete. Then we discuss various kinds of local consistency checks and in particular (2,3)-minimal instances. CSP hardness and bounded width
Sep. 25, 2018 1pm (MATH 350)	Ulam V. Baranovsky (UC Irvine) X Let (X, w) be a complex projective manifold with a holomorphic symplectic form w. Assume for simplicity that the space of holomorphic 2-forms on X is one-dimensional. Then it is known that (symplectic) deformations of the pair (X, w) are described by the Beauville-Bogomolov quadric Q in the second complex cohomology H2(X, C). The goal of the talk is to understand Q in terms of algebraic deformation theory and the fact that the Koszul bracket on the de Rham complex of X is homotopy abelian. Joint work with D. Kaledin. L-infinity morphisms and the Beauville-Bogomolov quadric
Sep. 25, 2018 2pm (MATH 350)	Lie Theory Michael Strayer (University of North Carolina at Chapel Hill) X R.M. Green axiomatically defined full heaps and used them to build minuscule-like representations of many affine Kac-Moody algebras. Two other classes of colored posets, namely minuscule and d-complete posets, have also been used in many applications to Lie theory; for instance, they correspond to “dominant minuscule” elements of Kac-Moody Weyl groups. We present new poset coloring properties that unify the above three classes of colored posets and characterize various Kac-Moody (sub)algebra representations. These include the full heap representations of Green, the minuscule representations of semisimple Lie algebras, and Demazure modules of dominant minuscule Weyl group elements. We will give the classifications of colored posets satisfying the two most important sets of these properties. Minuscule Kac-Moody settings unified by new poset coloring properties Sponsored by the Meyer Fund
Sep. 25, 2018 2pm (MATH 220)	Michael Wheeler (CU Boulder) The regular and good ultrapowers, Part 1
Sep. 25, 2018 3pm (Math 350)	Algebraic Geometry Leo Herr (University of Colorado, Boulder) X We will introduce a variant of Gromov-Witten Theory for log smooth curves, and compare invariants of a product of log smooth varieties with the invariants of each. To make this possible, we will give brief introductions to both Gromov-Witten Theory (curve counting) and Log Geometry. This variant of the theory originated in the work of M. Gross and B. Siebert, and we offer a new perspective on it, accompanied by new theorems. The Log Gromov-Witten Product Formula
Sep. 25, 2018 4pm (MATH 350)	Topology Robin Deeley (CU Boulder) X I will begin with a discussion on the basic properties of C-algebras with an emphasis on examples. Next the notions of essentially self-adjoint and essentially normal operator will be defined and relationship between these operators and K-homology with be developed. The talk will very much be an introduction and hence accessible to a wide audience. An introduction to C-algebras and K-homology
Sep. 26, 2018 4pm (MATH 350)	Grad Student Seminar Mark Pullins (CU Boulder) X Finite groups equipped with a sharply 2-transitive action have a useful, and simple, geometry associated to them. The geometry allows us to write the finite group as a semi-direct product and recover the structure of a near-field. In this talk, we examine the case of infinite groups with sharply 2-transitive actions. We will use the involutions to study the group, demonstrate how to construct a near field or near domain, and sketch a recent construction of an infinite sharply 2-transitive group that does not split. The Geometry of Sharply 2-Transitive Groups
Sep. 27, 2018 2pm (MATH 350)	Functional Analysis Robin Deeley (CU Boulder) X Smale spaces are a class of dynamical system defined by Ruelle to axiomatize properties of the basic sets of an Axiom A diffeomorphism. I will introduce Smale spaces by presenting three natural examples in detail. From a Smale space one can construct a number of C-algebras; each is obtained from an equivalence relation. These algebras will be discussed both in general and in the three aforementioned examples. Much of this talk is based on Ian Putnam's paper "C-algebras from Smale spaces". An introduction to Smale space C*-algebra

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