Stable Homotopy

Speaker: Enxin Wu (Western)

"Triangulated Categories"

Time: 14:00 - 15:00

Room: MC 108

I will talk about J.P. May's axioms of a triangulated category, present some properties and some basic examples (K(mathcal{A}) and D(mathcal{A})). This will be a start to the generalized stable homotopy theory in the sense of HPS (Hovey, Palmieri and Strickland).

Noncommutative Geometry

Speaker: Farzad Fathizadeh (Western)

"On the twisted local index formula in noncommutative geometry"

Time: 12:00 - 13:30

Room: MC 108

Analysis Seminar

Speaker: Rob Martin (UC Berkeley)

"Symmetric Operators and Reproducing Kernel Hilbert Spaces"

Time: 15:30 - 16:30

Room: MC 108

A reproducing kernel Hilbert space $H$ of functions on $\mathbb R$ which has a total orthogonal set of point evaluation vectors $(\delta_{x_{n}})$, $n\in Z$, is said to have the sampling property, since any $\phi\in H$ can be perfectly reconstructed from its `samples' or values taken on the set of points $(x_{n})$. The classic example of such a space is the Paley-Wiener space of $\Omega$-bandlimited functions. Such spaces are used extensively in applications including signal processing. In this talk we will apply the theory of self-adjoint extensions of symmetric operators to the study of such spaces. In particular, a sufficient operator-theoretic condition for a subspace of $L^{2}$ of the real line to be a reproducing kernel Hilbert space with the sampling property will be presented. Potential consequences for signal processing will be discussed.

Analysis Seminar

Speaker: Debraj Chakrabarti (Notre Dame)

"Function theory on Domains in Projective Space"

Time: 14:30 - 15:30

Room: MC 108

In this expository talk, we discuss some classical and recent results on holomorphic functions on subdomains of complex projective spaces. By a Theorem of Takeuchi, these domains are of two types : some on which all holomorphic functions are constant, and others on which there are many holomorphic functions. The main problem is to obtain a full geometric characterization of each type. This is related to the work of Lins-Neto, Siu and Shaw on non-existence of smooth Levi-Flat hypersurfaces in Projective space. Some conjectures in this direction are also discussed.

Stable Homotopy

Speaker: Enxin Wu (Western)

"Triangulated Categories II"

Time: 14:00 - 15:30

Room: MC 107

I will talk about a big class of examples for (pre)-triangulated categories -- the homotopy category of a pointed model category is a pre-triangulated category. I will start from the Reedy model structure and define framing on a (pointed) model category, roughly mention that Ho(mathcal{C}_*) is a closed Ho(sSet_*) module, and then define the loop and suspension functors, and also fiber and cofiber sequences.

Analysis Seminar

Speaker: Burglind Jöricke (IHES)

"Analytic continuation: from analysis to geometry"

Time: 15:30 - 16:30

Room: MC 108

Extension of analytic functions of one variable led to the notion of Riemann surfaces and has applications to many branches of mathematics. After a brief recollection I will focus on the effect in several complex variables which made the multi-dimensional theory geometric from the beginning and led to the notion of Stein manifolds and envelopes of holomorphy. I will describe a new construction of envelopes of holomorphy of domains in terms of equivalence classes of analytic discs.The construction is purely geometric and does not refer to the set of analytic functions in the domain. Several corollaries will be discussed.