Date: | September 22, 2017 |
Time: | 1:50PM - 2:50PM |
Location: | BLOC 628 |
Speaker: | Thomas Beck, MIT |
Title: | Ground state eigenfunctions on convex domains of high eccentricity |
Abstract: | In this talk, I will discuss the ground state eigenfunction of a class of Schrödinger operators on a convex planar domain. We will see how to construct two length scales and an orientation of the domain defined in terms of eigenvalues of associated differential operators. These length scales will determine the shape of the intermediate level sets of the eigenfunction, and as an application allow us to deduce properties of the first Dirichlet eigenfunction of the Laplacian for a class of three dimensional convex domains. In the two dimensional case, with constant potential, we will see that the eigenfunction satisfies a quantitative concavity property in a level set around its maximum, consistent with the shape of its intermediate level sets. |
Date: | September 22, 2017 |
Time: | 3:00PM - 4:00PM |
Location: | BLOC 117 |
Speaker: | Patrick Brosnan , University of Maryland |
Title: | Hessenberg varieties and a conjecture of Shareshian---Wachs |
Abstract: | I will explain joint work with Tim Chow proving a conjecture of Shareshian---Wachs which relates a combinatorial object, the so-called chromatic symmetric function of a certain graph, to a certain action of the symmetric on the cohomology of a Hessenberg variety first studied by J. Tymoczko. I should mention that, shortly after Chow and I posted our proof to the ArXiv, a completely independent proof relying on a map of Hopf algebras and the theorem of Aguiar---Bergeron---Sottile was posted by M. Guay-Paquet. The Hessenberg varieties in the title are certain smooth subvarieties of the the complete flag variety studied first by the applied mathematicians de Mari and Shayman. They were later generalized by de Mari, Procesi and Shayman to a setting where the general linear group is replaced with an arbitrary reductive group. In this case, Tymoczko's dot action becomes a representation of the Weyl group, and it is an interesting problem to determine this representation. I will present some results in this direction. In particular, I will explain a restriction formula that generalizes Guay-Paquet's proof that his Hopf algebra map respects comultiplication. |
Date: | September 22, 2017 |
Time: | 4:00PM - 5:00PM |
Location: | BLOC 628 |
Speaker: | V. Makam, U. Michicgan |
Title: | Degree bounds for invariant rings of quivers |
Abstract: | The ring of polynomial invariants for a rational representation of a reductive group is finitely generated. Nevertheless, it remains a difficult task to find a minimal set of generators, or even a bound on their degrees. Combining ideas originating from Hochster, Roberts and Kempf with the study of various ranks associated to linear matrices, we prove "polynomial" bounds for various invariant rings associated to quivers. The polynomiality of our bounds have strong consequences in algebraic complexity. If time permits, we will discuss these as well as applications to lower bounds for border rank of tensors. This is joint work with Derksen. |
Date: | September 22, 2017 |
Time: | 4:00PM - 5:00PM |
Location: | BLOC 220 |
Speaker: | Amudhan Krishnaswamy-Usha, TAMU |
Title: | Nilpotent elements of operator ideals are single commutators |
Abstract: | Pearcy and Topping asked in '71 if every compact operator can be written as a single additive commutator [B,C]=BC-CB of compact operators. While the general problem is still open, we show that every nilpotent operator in an operator ideal is a single commutator of operators from some power of the operator ideal; where the exponent depends on the degree of nilpotency. This is joint work with Ken Dykema. |
Date: | September 25, 2017 |
Time: | 3:00PM - 4:00PM |
Location: | BLOC 628 |
Speaker: | F. Gesmundo, Copenhagen |
Title: | On multiplicativity of various notions of rank |
Abstract: | Matrix rank has several different generalizations to the setting of tensors. Whereas for matrices it is easy to show that rank is multiplicative over tensor product (the matrix Kronecker product), multiplicativity is not straightforward (and in most cases false) in the setting of tensors. We discuss this problem for various notions of rank: tensor rank, partially symmetric tensor rank and tensor border rank in particular. The geometric framework allows for further generalizations, that we briefly present. |
Date: | September 25, 2017 |
Time: | 3:00PM - 4:00PM |
Location: | BLOC 220 |
Speaker: | Gilles Pisier, TAMU & Paris 6 |
Title: | Subgaussian random variables and generalizations |
Date: | September 25, 2017 |
Time: | 3:00PM - 3:50PM |
Location: | BLOC 624 |
Speaker: | Yongning Li, Texas A&M University |
Title: | Property (T) |
Date: | September 26, 2017 |
Time: | 3:00PM - 4:00PM |
Location: | BLOC 628 |
Speaker: | Giles Auchmuty, University of Houston |
Title: | Nonlinear PDEs Seminar |
Abstract: | Title: Energy Bounds for Planar Div-curl Boundary Value Problems |
Date: | September 26, 2017 |
Time: | 5:00PM - 6:00PM |
Location: | BLOC 628 |
Speaker: | E. Ventura, TAMU |
Title: | Hyperdeterminants II |
Date: | September 27, 2017 |
Time: | 1:45PM - 2:45PM |
Location: | BLOC 220 |
Speaker: | Oguz Gezmis, Texas A&M University |
Title: | De Rham isomorphism for Drinfeld modules over Tate algebras |
Abstract: | Two main concepts of the arithmetic on function fields are elliptic (Drinfeld) modules and L-Series. On 1970's, Drinfeld introduced elliptic modules which can be seen as an analogue of elliptic curves in function field setting and D. Goss introduced a new type of L-Series as an anologue of Rieamann Zeta Function. In 2012, Pellarin defined an L-series in Tate algebras which is a deformation of Goss's L-series. In order to give new identities for Pellarin L-Series, Angles, Pellarin and Tavares Ribeiro introduced Drinfeld modules over Tate algebras. In this talk, we talk about Drinfeld modules over Tate algebras of arbitrary rank. We also prove De Rham isomorphism for these modules under some conditions. Finally, we prove Legendre's Relation under this new setting. This is joint work with Matthew A. Papanikolas. |
Date: | September 27, 2017 |
Time: | 5:30PM - 6:30PM |
Location: | BLOC 628 |
Speaker: | Student Panel |
Title: | Panel discussion: adjusting to graduate school |
Date: | September 27, 2017 |
Time: | 6:00PM - 12:00PM |
Location: | BLOC 220 |
Speaker: | Dr. Negar Kalantar, Texas A&M University, Department of Architecture |
Title: | Things that Transform |
Abstract: | Physical transformation is all around us. However designers and engineers mainly focus on the object as an essentially static thing. How can the designer understand transformation itself as a parameter that can be shaped, and crafted? Transformation and motion have a strong bond with geometry because at its core, motion is the spatial transformation of one geometric configuration into another. In any transformation design process, there are two design efforts: the generation of an underlying geometry and the creation of an overlaid pattern. Therefore, knowing geometry is the key to transformable design. In another word, Transformation is where art, architecture, science and math merge. Dr. Kalantar with 17 years of experience in designing transformable structures will speak about her work in the field of Transformable Design ranging from a handheld toy to large structures. Also she will share: the geometric principles to create objects that change their size, shape, and surface; the principles of transformable design, such as underlying geometries and overlaid patterns; design principles of transformable polygons with scissor linkages. |
Date: | September 28, 2017 |
Time: | 3:00PM - 4:00PM |
Location: | BLOC 506A |
Speaker: | Rob Stevenson, University of Amsterdam |
Title: | An optimal adaptive Fictitious Domain Method |
Abstract: | We consider a Fictitious Domain formulation of an elliptic PDE, and solve the arising saddle-point problem by an inexact preconditioned Uzawa iteration. Solving the arising `inner' elliptic problems with an adaptive finite element method, we prove that the overall method converges with the best possible rate. So far our results apply to two-dimensional domains and lowest order finite elements (continuous piecewise linears on the fictitious domain, and piecewise constants on the boundary of the physical domain). Joint work with S. Berrone (Torino), A. Bonito (Texas A&M), and M. Verani (Milano). |
Date: | September 29, 2017 |
Time: | 1:50PM - 2:50PM |
Location: | BLOC 628 |
Speaker: | Gerardo Mendoza, Temple University |
Title: | TBA (joint with Several Complex Variables Seminar) |
Date: | September 29, 2017 |
Time: | 1:50PM - 2:50PM |
Location: | BLOC 628 |
Speaker: | Gerardo Mendoza, Temple University |
Title: | TBA (joint with MPHA Seminar) |
Date: | September 29, 2017 |
Time: | 3:00PM - 3:50PM |
Location: | BLOC 117 |
Speaker: | Sarah Witherspoon , Texas A&M University |
Title: | Algebraic deformation theory and the structure of Hochschild cohomology |
Abstract: | Some questions about deformations of algebras can be answered by using Hochschild cohomology, and in particular by using its Lie/Gerstenhaber brackets. Until very recently there was no independent description of this Lie structure for an arbitrary resolution, a big disadvantage both theoretically and computationally. In this talk, we will first introduce Hochschild cohomology and explain its role in algebraic deformation theory. We will then summarize recent progress by several mathematicians, focusing on examples. |
Date: | September 29, 2017 |
Time: | 4:00PM - 5:00PM |
Location: | BLOC 628 |
Speaker: | JM Landsberg, TAMU |
Title: | Quantum max flow v. quantum min cut and the geometry of matrix product states |
Date: | September 29, 2017 |
Time: | 4:00PM - 5:00PM |
Location: | BLOC 220 |
Speaker: | Scott LaLonde, University of Texas at Tyler |
Title: | TBA |
Abstract: | TBA |
Date: | October 2, 2017 |
Time: | 3:00PM - 4:00PM |
Location: | BLOC 220 |
Speaker: | Eviatar Procaccia, TAMU |
Title: | TBA |
Abstract: | TBA |
Date: | October 2, 2017 |
Time: | 3:00PM - 4:00PM |
Location: | BLOC 628 |
Speaker: | Tian Yang, TAMU |
Title: | TBA |
Date: | October 2, 2017 |
Time: | 3:00PM - 3:50PM |
Location: | BLOC 624 |
Speaker: | Jintao Deng, Texas A&M University |
Title: | Property A II |
Date: | October 2, 2017 |
Time: | 4:00PM - 5:00PM |
Location: | Blocker 117 |
Speaker: | David Kribs, University of Guelph |
Title: | Quantum Information: A (Brief) Mathematical Introduction |
Abstract: | Quantum information is an umbrella term that is used to encompass such topics as quantum computing, quantum cryptography, quantum information theory, quantum error correction, quantum entanglement theory, and quantum information processing. In this talk, I will give a brief introduction to as many fundamental topics in quantum information that I can possibly fit into one talk. I'll start by going through the formulation of quantum information from postulates of quantum mechanics, with emphasis on the linear algebra and operator theoretic perspective. Time dependent, I will then touch on aspects of quantum entanglement theory, quantum algorithms and universal sets of unitary gates, quantum error correction, and quantum privacy. |
Date: | October 3, 2017 |
Time: | 4:00PM - 5:00PM |
Location: | Blocker 117 |
Speaker: | David Kribs, University of Guelph |
Title: | Quantum Error Correction |
Abstract: | Quantum error correction as a field of study goes back over two decades, growing out of early attempts to build small-scale quantum computers and develop a theoretical underpinning for experimental attempts to control features of evolving quantum systems. The subject has since seen significant development and now connects with every area of quantum information science. In this talk, I will give an introduction to quantum error correction through a mathematical lens. I will focus on the basic framework, and touch on examples and results that involve aspects of group theory, matrix theory, and operator algebras. |
Date: | October 4, 2017 |
Time: | 6:00PM - 00:00AM |
Location: | BLOC 220 |
Speaker: | Dr. Peter Howard, Texas A&M University, Department of Mathematcis |
Title: | The Mathematics of Games of Chance |
Abstract: | Following early work by the Italian mathematician, physician, astrologer, and all around sketchy character Gerolamo Cardano, the classical theory of probability was developed in large part as an uneasy collaboration between professional gamblers such as Antoine Gombaud, and a coterie of brilliant French noblemen looking for just about any excuse to prove how smart they were (I'm looking at you, Pierre-Simon, Marquis de Laplace). In this talk, I'll give an overview of the early development of probability theory, and talk about applications to games of chance such as Roulette and Blackjack. Texas Hold'em will be mentioned as an invitation to study game theory. |
Date: | October 5, 2017 |
Time: | 4:00PM - 5:00PM |
Location: | Blocker 117 |
Speaker: | David Kribs, University of Guelph |
Title: | Quantum Privacy and Complementarity |
Abstract: | The first significant real-world applications of quantum information appear to be around the corner in the realm of cryptography and communication privacy. Private quantum channels and codes are a fundamental notion in quantum privacy, initially discovered almost two decades ago through efforts to construct quantum analogues of the classical one-time pad. In recent years the subject has blossomed, with a new focus on the development of a structure theory for private quantum codes. These recent efforts have partly been motivated by a realization that private quantum codes are complementary, in a mathematically explicit way, to quantum error correcting codes. I will give an introduction to the topic in this talk, with focus on mathematical aspects of the emerging theory and connections with quantum error correction. |
Date: | October 6, 2017 |
Time: | 3:00PM - 4:00PM |
Location: | BLOC 117 |
Speaker: | Tian Yang, Texas A&M University |
Title: | TBA |
Date: | October 6, 2017 |
Time: | 4:00PM - 5:00PM |
Location: | BLOC 628 |
Speaker: | Boris Hanin, TAMU |
Title: | TBA |
Date: | October 11, 2017 |
Time: | 6:00PM - 00:00AM |
Location: | BLOC 220 |
Speaker: | Dr. Alireza Talebpour, Texas A&M University, Department of Civil Engineering |
Title: | TBA |
Date: | October 13, 2017 |
Time: | 1:00PM - 2:00PM |
Location: | BLOC 220 |
Speaker: | Dinesh Thakur, University of Rochester |
Title: | TBA |
Date: | October 13, 2017 |
Time: | 1:50PM - 2:50PM |
Location: | BLOC 628 |
Speaker: | Dmitri Pelinovsky, McMaster University |
Title: | TBA |
Date: | October 13, 2017 |
Time: | 3:00PM - 4:00PM |
Location: | BLOC 117 |
Speaker: | Yiby Morales, Universidad de los Andes |
Title: | TBA |
Date: | October 13, 2017 |
Time: | 4:00PM - 5:00PM |
Location: | BLOC 220 |
Speaker: | Mehrdad Kalantar, University of Houston |
Title: | TBA |
Abstract: | TBA |
Date: | October 13, 2017 |
Time: | 4:00PM - 5:00PM |
Location: | BLOC 628 |
Speaker: | Emre Sen, Northeastern |
Title: | TBA |
Date: | October 16, 2017 |
Time: | 3:00PM - 4:00PM |
Location: | BLOC 628 |
Speaker: | Zheng Zhang, TAMU |
Title: | TBA |
Date: | October 18, 2017 |
Time: | 1:45PM - 2:45PM |
Location: | BLOC 220 |
Speaker: | Junehyuk Jung, Texas A&M University |
Title: | TBA |
Date: | October 18, 2017 |
Time: | 6:00PM - 00:00AM |
Location: | BLOC 220 |
Speaker: | Dr. Prabir Daripa, Texas A&M University, Department of Mathematics |
Title: | TBA |
Date: | October 20, 2017 |
Time: | 3:00PM - 3:50PM |
Location: | BLOC 117 |
Speaker: | Benjamin Schröter, TU-Berlin |
Title: | Multi-splits in hypersimplicies and split matroids |
Abstract: | Multi-splits are a class of coarsest regular subdivisions of convex polytopes. In this talk I will present a characterization of all multi-splits of two types of polytopes, namely products of simplices and hypersimplices. It turns out that the multi-splits of these polytopes are in correspondence with one another and matroid theory is the key in their analysis, as all cells in a multi-split of a hypersimplex are matroid polytopes. Conversely, the simplest case of multi-splits of hypersimplices give rise to a new class of matroids, which we call split matroids. The structural properties of split matroids can be exploited to obtain new results in tropical geometry. |
Date: | October 20, 2017 |
Time: | 4:00PM - 5:00PM |
Location: | BLOC 628 |
Speaker: | Michael Di Pasquale, Oklahoma State University |
Title: | Homological Obstructions to Freeness of Multi-arrangements |
Abstract: | If the module of vector fields tangent to a multi-arrangement is free over the underlying polynomial ring, we say that the multi-arrangement is free. It is of particular interest in the theory of hyperplane arrangements to investigate the relation of freeness to the combinatorics of the intersection lattice - the holy grail here is Terao's conjecture that freeness of arrangements is detectable from the intersection lattice. It is known that corresponding statements for multi-arrangements fail. Given a multi-arrangement, we present a co-chain complex derived from work of Brandt and Terao on k-formality whose exactness encodes freeness of the multi-arrangement. The cohomology groups of this co-chain complex thus present obstructions to freeness of multi-arrangements. Using this criterion we give an example showing that the property of being totally non-free is not detectable from the intersection lattice. This builds on previous work with Francisco, Schweig, Mermin, and Wakefield. |