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Department of Mathematics


Colloquia and Seminars

The Department of Mathematics is home to a dynamic group of scholars who regularly share their expertise with others. Many of our events and activities are free and open to the public, and we encourage you to get involved.

October

OCT 30 - Algebraic Geometry Seminar: Cubic surfaces in positive characteristic

When: Monday, October 30, 2017 - 3:30 p.m.
When: LeConte 317R (map)

Speaker: Alexander Duncan, University of South Carolina

Abstract: I describe the possible automorphism groups of a cubic surface over an algebraically closed field of arbitrary characteristic. We will see that, while the actual groups that appear in different characteristics can vary considerably, the differences can all be explained by a handful of simple geometric observations.

Pretalk: Given two curves in the complex projective plane, Bezout's theorem provides a simple formula for the number of intersection points (counting multiplicities). The goal of intersection theory is to generalize this idea to intersections of subvarieties of more general varieties. I will discuss the intersection theory of surfaces with an eye towards describing the configuration of 27 lines on a cubic surface.

OCT 31 - Graduate Colloquium: Classification of Elementary Particles via Symplectic Induction

When: Tuesday, October 31, 2017 - 4:30 p.m. to 5:30 p.m.
When: LeConte 412 (map)

Speaker: Kaller Vandebogert

Abstract: The Poincare group G has a linear representation which can be understood as the composition of a Lorentz transform and a spacetime "boost" for points sitting in Minkowski space. As it turns out, the (abelian) normal subgroup of spacetime boosts H induces a particularly simple orbit structure of our Poincare group, but only for elements of H. Luckily, there is an elaborate construction known as Symplectic Induction for which you can induce a symplectic structure on the entirety of a space based off of the symplectic structure of H-orbits. These induced orbits allow us to classify the standard elementary particles: photons, tachyons, and particles with mass, and characterize these systems as Hamiltonian G-spaces.

(This talk will be made as accessible as possible, but some familiarity with Lie groups/algebras and coadjoint representations would certainly help!)

 

November

NOV 7 - Graduate Colloquium: Syzygies

When: Tuesday, November 7, 2017 - 4:30 p.m. to 5:30 p.m.
When: LeConte 412 (map)

Speaker: Andy Kustin

Abstract: Hilbert introduced the notion of ``syzygies'' in his 1890 paper ``Ueber die Theorie der algebraischen Formen''. This paper contains the proof of the Hilbert basis theorem, the proof of the Hilbert syzygy theorem, the proof of Hilbert's Nullstellensatz, and the first version of the Hilbert-Burch theorem. Hilbert's motivation was combinatorial. He wanted to count how many homogeneous forms of each degree live in a given ring of invariants. 

In this talk, syzygies will introduced slowly and gently. Various applications of syzygies to combinatorics, algebraic topology, and algebraic geometry will be described. For example, information about the singularities of a parameterized curve can be read from the syzygies of the parameterizing functions. Also, the syzygies of the homogeneous coordinate ring of a variety encode geometric information about the variety. Finally, there will be a discussion about how to find syzygies. We will discuss the Nike method, techniques from combinatorics and algebraic topology, computational techniques (that is, Groebner bases), and the geometric method. I am offering a course on the geometric method for finding syzygies in the Spring of 2018. The course and the textbook are both called ``The cohomology of vector bundles and syzygies''.

NOV 14 - Graduate Colloquium: Toric Varieties

When: Tuesday, November 14, 2017 - 4:30 p.m. to 5:30 p.m.
When: LeConte 412 (map)

Speaker: Alicia Lamarche

December

DEC 7 - Discrete Scalar Quantum Field Theory

When: Thursday, December 7, 2017 - 4:30 p.m. to 5:30 p.m.
When: LeConte 412 (map)

Speaker: Stan Gudder, University of Denver

Abstract: This talk is meant for a general audience and no prior knowledge of physics is required. We begin by assuming that spacetime is discrete and is described by a 4-dimensional cubic lattice. This implies that there are discrete sets of possible particle energies, momenta and masses. We then define discrete scalar quantum fi elds. These fi elds are employed to construct interaction Hamiltonians and scattering operators. Besides discreteness, our main assumption is conservation of energy-momentum for a scattering process. We conclude with various examples of perturbation approximations. These include simplifi ed versions of electron-electron and electron-proton scattering as well as simple decay processes. We also define scattering cross-sections, decay rates and lifetimes within this formalism. [PDF]

Host: George Androulakis

 

January

JAN 25 - Zhen-qing Chen

When: Thursday, January 25, 2018  - 4:30 p.m. to 5:30 p.m.
When: LeConte 412 (map)

Speaker: Zhen-qing Chen, University of Washington

Abstract: TBA

Host: TBA

 

February

FEB 22 - Danny Krashen

When: Thursday, February 22, 2018  - 4:30 p.m. to 5:30 p.m.
When: LeConte 412 (map)

Speaker: Danny Krashen, Rutgers University / University of Georgia

Abstract: TBA

Host: Frank Thorne

 

March

MARCH 1 - Lars Christensen

When:  Thursday, March 1, 2018  - 4:30 p.m. to 5:30 p.m.
When: LeConte 412 (map)

Speaker: Lars Christensen, Texas Tech University

Abstract: TBA

Host: Adela Vraciu