Geometry Seminar
Format: Talks are 50-60 minutes, with the option to continue after a
short break.
How to
Give a Good Colloquium by John E. McCarthy.

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Date Time |
Location | Speaker |
Title – click for abstract |
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01/27 4:00pm |
MILN 216 |
Jaydeep Chipalkatti University of Manitoba |
On Hilbert Covariants
Let F(x_1,x_2)
denote a homogeneous binary form of order $d$. Assume
that d factors as d= rm. The Hilbert covariant
H_{r,d}(F) is a binary form (whose coefficients are polynomials
in the coefficients of F) with the following property:
H_{r,d}(F) vanishes identically, exactly when F is a
perfect m-th power of an order r form. It was constructed by
Hilbert in 1885; and in particular, H_{1,d}(F) is the
Hessian of F.
In geometric terms, we have an SL_2-equivariant imbedding of
P^r into P^d, and the coefficients of H_{r,d} give a set of
defining equations for the image variety. These covariants are
part of a beautiful classical landscape called the 'invariant theory of binary
forms', whose origins lie in the mid-19th century.
In this talk, I will exhibit two entirely different approaches to the construction of H, and outline a proof of the fact that they lead to the
same object. I will also mention some results and problems about the ideal generated
by the coefficients of H. All of this is joint work with Abdelmalek Abdesselam from the University of Virginia. |
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01/30 4:00pm |
MIST 102 |
Mboyo Esole Harvard U. |
Elliptic fibrations and string theory-- joint with Physics
Elliptic curves are an important subject in many branches of mathematics from number theory to algebraic geometry and cryptography. They also play a central role in several questions of theoretical physics, specially in string theory.
In this talk, I will review certain aspects of the geometry of elliptic fibrations and explain how recent questions in string theory challenge the traditional treatment of these types of geometry and inspire new directions of research for mathematicians.
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02/17 4:00pm |
U. Houston |
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Texas Geometry and Topology Conference, Feb 17 - 19
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02/20 4:00pm |
MILN 216 |
Tamar Friedmann U. Rochester |
TBA -- joint with Physics |
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03/02 4:00pm |
MILN 216 |
Radu Laza SUNY Stony Brook |
Semi-algebraic horizontal subvarieties of Calabi-Yau type
Except a few special cases (e.g. abelian varieties and K3 surfaces), the
images of period maps for families of algebraic varieties satisfy
non-trivial Griffiths' transversality relations. It is of interest to
understand these images of period maps, especially for Calabi-Yau
threefolds. In this talk, I will discuss the case when the images of
period maps can be described algebraically. Specifically, I will show
that if a horizontal subvariety Z of a period domain D is semi-algebraic
and is stabilized by a large discrete group, then Z is automatically
Hermitian symmetric with a totally geodesic embedding into the period
domain D. Additionally, I will discuss the classification of the
semi-algebraic cases for variations of Hodge structures of Calabi-Yau
type. This is joint work with R. Friedman. |
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03/16 4:00pm |
MILN 216 |
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Spring Break -- no seminar |
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04/20 4:00pm |
MILN 216 |
Sema Salur U. Rochester |
TBA |
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04/26 4:00pm |
TAMU |
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Pre-TAGS Workshop (Thu-Fri)
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04/27 4:00pm |
TAMU |
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Texas Algebraic Geometry Seminar (Fri-Sun)
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Archives
Please contact
Colleen Robles
for more information.