Seminar Calendar
for Graduate Geometry and Topology Seminar events the year of Saturday, July 21, 2012.

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More information on this calendar program is available.
Questions regarding events or the calendar should be directed to Tori Corkery. 
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Thursday, January 19, 2012

Graduate Geometry and Topology Seminar
2:00 pm   in 241 Altgeld Hall,  Thursday, January 19, 2012
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Submitted by lukyane2.
Organizational Meeting
Abstract: Organizational meeting for the seminar.

Thursday, January 26, 2012

Graduate Geometry and Topology Seminar
2:00 pm   in 241 Altgeld Hall,  Thursday, January 26, 2012
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Submitted by lukyane2.
Mee Seong Im (UIUC Math)
The Hamiltonian reduction of a certain affine variety
Abstract: I will discuss certain theories in symplectic geometry and in algebraic geometry which give us various ways to view the same complex manifold. More specifically, the Hamiltonian reduction of the cotangent bundle of a certain variety can be thought of as the symmetric product of the complex plane while the GIT quotient of the same cotangent bundle but which is twisted by a character of the general linear group can be thought of as a certain Hilbert scheme. These varieties are related by the Hilbert-Chow morphism in the sense that one is a desingularization of the other. I will end with an analogous construction in which a notion of noncommutativity appears in the algebro-geometric quotient. Lots of examples will be provided throughout my talk.

Thursday, February 2, 2012

Graduate Geometry and Topology Seminar
2:00 pm   in 241 Altgeld Hall,  Thursday, February 2, 2012
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Submitted by lukyane2.
Ser-Wei Fu (UIUC Math)
Length Spectra and Deformation Families
Abstract: This is a practice talk for the preliminary exam. I will define and describe the spectral rigidity problem and talk about known results. The talk will be focused on clearly defining every object and giving examples to illustrate a new approach to the problem. To be specific, two main topics that will be discussed are flat metrics and train tracks on surfaces.

Thursday, February 9, 2012

Graduate Geometry and Topology Seminar
2:00 pm   in 241 Altgeld Hall,  Thursday, February 9, 2012
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Submitted by lukyane2.
Michael DiPasquale (UIUC Math)
Resolutions and Geometry
Abstract: Given a variety X inside of some projective space, one of the primary ways in which algebraic geometers study X is through its homogeneous coordinate ring S_X. One way to unpack the information hiding mysteriously inside of S_X is to study the free resolution of S_X. From this resolution come many fantastic invariants of X, primarily the betti diagram of X from which one can compute the Hilbert function of X and the regularity of X. Many difficult open conjectures for curves relate to the configuration of the betti diagram of the curve. Our modest goal is to see how such a seemingly arcane algebraic object as a resolution can actually reflect the geometry of a variety, primarily by looking at the case where X is a bunch of points in projective space. Interested folks may find David Eisenbud's book Geometry of Syzygies a good read; that is where much of my material will come from.

Thursday, February 16, 2012

Graduate Geometry and Topology Seminar
2:00 pm   in 241 Altgeld Hall,  Thursday, February 16, 2012
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Submitted by lukyane2.
Jimmy Shan (UIUC Math)
Polytopes, zeroes of polynomial equations and mixed volume
Abstract: We will present a bound of number of zeroes of polynomial equations using mixed volumes of polytopes which are constructed from the exponent vectors of the polynomials; Newton polytope associated to one polynomial is a prototype.

Thursday, February 23, 2012

Graduate Geometry and Topology Seminar
2:00 pm   in 241 Altgeld Hall,  Thursday, February 23, 2012
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Submitted by lukyane2.
Brian Collier (UIUC Math)
Motivating Hamiltonian Floer Theory
Abstract: The focus of this talk will be to motivate the main ideas in Hamiltonian Floer theory. To start, we will review the notion of a Hamiltonian vector field and other important things in symplectic geometry. We will then talk about Morse Theory in a manner that will generalize most naturally to the infinite dimensional situation. Finally I will introduce Hamiltonian Floer Theory as the analog of the Morse theory of a certain action functional.

Thursday, March 1, 2012

Graduate Geometry and Topology Seminar
2:00 pm   in 241 Altgeld Hall,  Thursday, March 1, 2012
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Submitted by lukyane2.
Juan Villeta-Garcia (Department of Mathematics, University of Illinois at Urbana-Champaign)
The Harder-Narasimhan stratification of quiver representations
Abstract: A quiver is a finite graph with orientations, and their representations are defined by assigning vector spaces to each vertex and linear maps to each arrow. The theory of quiver representations is incredibly broad, with applications to such areas as quantum physics, Lie theory and invariant theory. We will give a brief overview of the category of quiver representations, and use a construction of Reineke that mimics the Harder-Narasimhan filtration for vector bundles, to analyze this category.

Thursday, March 8, 2012

Graduate Geometry and Topology Seminar
2:00 pm   in 241 Altgeld Hall,  Thursday, March 8, 2012
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Submitted by lukyane2.
Sarah Yeakel (Department of Mathematics, University of Illinois at Urbana-Champaign)
Spectra
Abstract: I'll define spectra with motivation from homotopy theory, explain why they form a nicer category than topological spaces, and talk about how they are useful tools in pretty much any setting with a (co)homology theory.

Thursday, March 15, 2012

Graduate Geometry and Topology Seminar
2:00 pm   in 241 Altgeld Hall,  Thursday, March 15, 2012
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Submitted by lukyane2.
Peter Nelson (Department of Mathematics, University of Illinois at Urbana-Champaign)
Formal groups in algebraic topology
Abstract: Formal groups are objects that lie between Lie groups and Lie algebras. I'll motivate their application to geometry and topology by discussing Chern classes of vector bundles. Then I'll talk about their role in algebraic topology. This theory provides a deep connection between topology and algebraic geometry and even number theory.

Thursday, March 29, 2012

Graduate Geometry and Topology Seminar
2:00 pm   in 241 Altgeld Hall,  Thursday, March 29, 2012
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Submitted by lukyane2.
Santiago Camacho (UIUC Math)
Some first order definable properties of Tropical Geometry
Abstract: There are many different ways one can approach tropical geometry, approximation by amoebas generated by algebraic varieties in $\mathbb{C}^n$, the valuation map over algebraic varieties of general algebraically closed valued fields, or just simply the geometry of the min-plus tropical semiring of $\mathbb{R}$. On this talk we focus on these last two and give a sketch of a proof of the fundamental theorem of tropical geometry linking them together, using elementary model theoretic tools. No previous knowledge on logic will be a assumed.

Thursday, April 5, 2012

Graduate Geometry and Topology Seminar
2:00 pm   in 241 Altgeld Hall,  Thursday, April 5, 2012
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Submitted by lukyane2.
Grace Work (UIUC Math)
Ideal Triangulations of Hyperbolic 3-Manifolds
Abstract: In this talk we will see how link complements can be decomposed into finite unions of ideal tetrahedra. From this decomposition we can compute the hyperbolic structure on these manifolds. The tetrahedra provide us with information we can use to compute arithmetic invariants of the manifolds. Our main example will be the complement of the figure-eight knot.

Thursday, April 12, 2012

Graduate Geometry and Topology Seminar
2:00 pm   in 241 Altgeld Hall,  Thursday, April 12, 2012
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Submitted by lukyane2.
Kelly Funk (Department of Mathematics, University of Illinois at Urbana-Champaign)
Rigidity Across Dynamics
Abstract: We will discuss the notions of rigidity and uniform rigidity for dynamical systems. We will explore the structure of these sequences and attempt to characterize them.

Thursday, April 19, 2012

Graduate Geometry and Topology Seminar
2:00 pm   in 241 Altgeld Hall,  Thursday, April 19, 2012
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Submitted by lukyane2.
Francesco Bei (Sapienza Università di Roma)
L^2 de Rham and Hodge theorems on stratified pseudomanifolds
Abstract: Even when studying smooth objects one often runs into singular spaces, but fortunately these often come with some extra structure: a stratification. After recalling what a stratification is and how they come up, I will show that there exist a class of Riemannian metrics whose L^2 de Rham and Hodge cohomology groups are isomorphic to certain topologically defined intersection cohomology groups with a `perversity' that depends on the metric.

Thursday, April 26, 2012

Graduate Geometry and Topology Seminar
2:00 pm   in 241 Altgeld Hall,  Thursday, April 26, 2012
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Submitted by lukyane2.
Caglar Uyanik (Department of Mathematics, University of Illinois at Urbana-Champaign)
What is an Outer Space?
Abstract: I will try to explain the construction and the topology of Outer space introduced by Culler and Vogtmann. In particular, I will sketch the proof of contractibility.

Thursday, May 3, 2012

Special Graduate Geometry and Topology Seminar
12:00 pm   in 241 Altgeld Hall,  Thursday, May 3, 2012
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Submitted by lukyane2.
Amir Nayyeri (UIUC Computer Science)
How to Walk Your Dog in the Mountains
Abstract: We describe a O(log n)-approximation algorithm for computing the homotopic Frechet distance between two polygonal curves that lie on the boundary of a surface. Prior to this work, algorithms where known only for curves on the Euclidean plane with polygonal obstacles. A key technical ingredient in our analysis is a $O(\log n)$-approximation algorithm for computing the minimum height of a homotopy between two curves. No algorithms were previously known for approximating this parameter. Surprisingly, it is not even known if computing either the homotopic Frechet distance, or the minimum height of a homotopy, is in NP. Joint work with Sariel Har-Peled, Mohammad Salavatipour and Anastasios Sidiropoulos

Thursday, August 30, 2012

Graduate Geometry Topology Seminar
2:00 pm   in 241 Altgeld Hall,  Thursday, August 30, 2012
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Submitted by collier3.
Informational and Organizational meeting
Abstract: It's time for the graduate geometry and topology seminar to start again. We will meet for a short organizational meeting. Everyone in strongly encouraged to attend, especially new first years. COOKIES will be provided.