Past Junior Geometry and Topology Seminar

29 April 2010
12:00
Maria Buzano
Abstract
The aim of this talk is to get a feel for the Ricci flow. The Ricci flow was introduced by Hamilton in 1982 and was later used by Perelman to prove the Poincaré conjecture. We will introduce the notions of Ricci flow and Ricci soliton, giving simple examples in low dimension. We will also discuss briefly other types of geometric flows one can consider.
  • Junior Geometry and Topology Seminar
4 March 2010
12:00
Michael Groechenig
Abstract
Descent theory is the art of gluing local data together to global data. Beside of being an invaluable tool for the working geometer, the descent philosophy has changed our perception of space and topology. In this talk I will introduce the audience to the basic results of scheme and descent theory and explain how those can be applied to concrete examples.
  • Junior Geometry and Topology Seminar
25 February 2010
12:00
Jessica Banks
Abstract
In 2008, Juhasz published the following result, which was proved using sutured Floer homology. Let $K$ be a prime, alternating knot. Let $a$ be the leading coefficient of the Alexander polynomial of $K$. If $|a|<4$, then $K$ has a unique minimal genus Seifert surface. We present a new, more direct, proof of this result that works by counting trees in digraphs with certain properties. We also give a finiteness result for these digraphs.
  • Junior Geometry and Topology Seminar
18 February 2010
12:00
to
18 March 2010
13:00
Laura Schaposnik
Abstract
We will consider the monodromy action on mod 2 cohomology for SL(2) Hitchin systems. We will study Copeland's approach to the subject and use his results to compute the monodromy action on mod 2 cohomology. An interpretation of our results in terms of geometric properties of fixed points of a natural involution on the moduli space is given.
  • Junior Geometry and Topology Seminar
11 February 2010
12:00
Hwasung Mars Lee
Abstract
We will present a physical motivation of the SYZ conjecture and try to understand the conjecture via calibrated geometry. We will define calibrated submanifolds, and also give sketch proofs of some properties of the moduli space of special Lagrangian submanifolds. The talk will be elementary and accessible to a broad audience.
  • Junior Geometry and Topology Seminar
4 February 2010
12:00
Imran Qureshi
Abstract
Many interesting classes of projective varieties can be studied in terms of their graded rings. For weighted projective varieties, this has been done in the past in relatively low codimension. Let $G$ be a simple and simply connected Lie group and $P$ be a parabolic subgroup of $G$, then homogeneous space $G/P$ is a projective subvariety of $\mathbb{P}(V)$ for some\\ $G$-representation $V$. I will describe weighted projective analogues of these spaces and give the corresponding Hilbert series formula for this construction. I will also show how one may use such spaces as ambient spaces to construct weighted projective varieties of higher codimension.
  • Junior Geometry and Topology Seminar
28 January 2010
13:15
Steven Rayan
Abstract
After reviewing the salient details from last week's seminar, I will construct an explicit example of a spectral curve, using co-Higgs bundles of rank 2. The role of the spectral curve in understanding the moduli space will be made clear by appealing to the Hitchin fibration, and from there inferences (some of them very concrete) can be made about the structure of the moduli space. I will make some conjectures about the higher-dimensional picture, and also try to show how spectral varieties might live in that picture.
  • Junior Geometry and Topology Seminar

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