Format: Talks are 50-60 minutes, with the option to continue after a
short break.
Joint Geometry-Physics Seminar: Approximately once a month the geometry group meets
with the Physics
Department for seminar.
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Date Time |
Location | Speaker |
Title – click for abstract |
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09/11 4:00pm |
MILN 216 |
Jan Draisma Technische Universiteit |
Finiteness of the k-factor model
The polynomial ring C[x_1,x_2,...] of polynomials with complex
coefficients in countably many variables is not Noetherian. However,
a beautiful result by Aschenbrenner and Hillar says that ideals that are
stable under all permutations of the coordinates x_1,x_2,... do have a
finite generating set up to coordinate permutations. This result lies at
the heart of several recent finiteness results for chains of algebraic
varieties arising from applications, e.g. in algebraic statistics. I
will sketch some of the methods, both theoretical and computational,
by means of one such result: finiteness for the k-factor model. |
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10/07 3:00pm |
MILN 313 |
L. Oeding U. Florence |
The Chow variety of zero cycles |
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10/08 2:00pm |
Miln 317 |
A. Ginesky WH Trading |
Determinantal Equations for Curves and their Secant Varieties |
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10/09 2:00pm |
MILN 313 |
J.M. Landsberg TAMU |
Geometry and P v.s. NP |
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10/09 4:00pm |
MILN 216 |
Leobardo Rosales Rice U. |
The Two-Valued Minimal Surface Equation
We discuss a PDE method for producing examples of immersed minimal surfaces in the unit cylinder in $\mathbb{R}^{3},$ as the graph of two-valued functions over the punctured unit disk. These two-valued functions can either be extended continuously across the origin, in which case the two-valued graph is a stable branched minimal immersion, or we can give an asymptotic description of the graphs near the vertical axis. Various analogies to the theory of the Minimal Surface Equation will be illustrated.
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10/16 4:00pm |
MILN 216 |
Daniel Allcock U. Texas, Austin |
The monodromy of the Hurwitz space over the moduli space of points in CP1
The Hurwitz space H means the space of all covers of CP1 with given
degree D and simple branching over N points. It is a non-Galois unramified
cover of the moduli space M of unordered N-tuples in CP1. We explain the
monodromy action of the base on the fiber, in the case D=4. Equivalently, we
find the Galois group of the Galois cover associated to H-->M. |
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10/30 4:00pm |
MILN 216 |
Mark Sepanski Baylor University |
On the L-S category of Lie groups.
The (normalized) Lusternik-Schnirelmann category of a topological space X, denoted cat(X), is the least integer m such that X can be covered by m + 1 open sets that are contractible in X. One of the problems on Ganea’s list from 1971 asks to find the L-S category of (compact) Lie groups.
In joint work with M. Hunziker, we show that the L-S category of a simple, simply connected, compact Lie group G is bounded above by the sum of the relative categories of certain distinguished conjugacy classes in G corresponding to the vertices of the fundamental alcove for the action of the affine Weyl group on the Lie algebra of a maximal torus of G.
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11/06 4:00pm |
MILN 216 |
Christopher Manon MSRI |
Phylogenetic algebraic geometry and the Verlinde formula
Recent work of Sturmfels and Xu establishes an intriguing connection between the Hilbert functions of important projective varieties from phylogenetic algebraic geometry and a genus 0, sl_2(\C) case of the celebrated Verlinde formula from mathematical physics. We will discuss how this relationship can be constructed and generalized with the representation theory of affine Kac-Moody algebras and the associated theory of conformal blocks. |
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11/07 9:00pm |
Rice U |
Texas Geometry & Topology Conference Nov 6--8 |
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11/13 4:00pm |
MILN 216 |
Gavin Brown University of Kent at Canterbury |
Gorenstein models of complex 3-folds of general type.
A (minimal) complex algebraic manifold is of general type
if its canonical class (the determinant line bundle of the
cotangent bundle) is positive. This is the typical behaviour,
often interpreted loosely as being the hyperbolic case.
Such manifolds have canonical embeddings into (weighted)
projective space, simplifying questions of isomorphism
and classification. Given equations of a manifold in
some embedding, it is possible to compute the canonical
embedding using various computer algebra packages.
The images of these embeddings are defined by Gorenstein
systems of equations. The easiest cases of this are
when the image is cut out by one or two independent
equations. Such complete intersection 3-folds of general
type have been the subject of lists (by Reid and Fletcher
in the 1980s) that were recently shown to be complete
(by Chen-Chen-Chen).
Turning the question around, I consider more complicated
systems of Gorenstein equations, and construct analogous
classifications of orbifold 3-folds in higher codimension. |
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11/20 4:00pm |
MILN 216 |
J. Clelland U. Colorado |
Backlund transformations and Darboux integrability for nonlinear wave equations
We prove that a second-order Monge-Ampere equation for one function of two variables is connected to the flat wave equation by a Backlund transformation if and only if it is integrable by the method of Darboux at second order. The proof relies on a geometric formulation of a Backlund transformation as a certain type of exterior differential system and its associated differential invariants. This is joint work with Thomas Ivey of The College of Charleston. |
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12/04 4:00pm |
MILN 216 |
Leonardo Mihalcea Baylor University |
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