Abstract: Modal logic is used to study various modalities, i.e. various ways in which statements can be true, the most notable of which are the modalities of necessity and possibility. In set-theory, a natural interpretation is to consider a statement as necessary if it holds in any forcing extension of the world, and possible if it holds in some forcing extension. One can now ask what are the modal principles which captures this interpretation, or in other words - what is the "Modal Logic of Forcing"?
Title: Local root numbers for Heisenberg representations
Abstract: On the Langlands program, explicit computation of the local root numbers (or epsilon factors) for Galois representations is an integral part. But for arbitrary Galois representation of higher dimension, we do not have explicit formula for local root numbers. In our recent work (joint with Ernst-Wilhelm Zink) we consider Heisenberg representation (i.e., it represents commutators by scalar matrices) of the Weil
Abstract: we give an overview of Gowers' proof for the existence of 4-term progression in subsets of positive density in the integers. We will discuss the tools from additive combinatorics that are used in the proof as well as some related conjectures.
Abstract: we give an overview of Gowers' proof for the existence of 4-term progression in subsets of positive density in the integers. We will discuss the tools from additive combinatorics that are used in the proof as well as some related conjectures.
Title: Irreducibility of Galois representations associated to low weight Siegel modular forms
Abstract: If f is a cuspidal modular eigenform of weight k>1, Ribet proved that its associated p-adic Galois representation is irreducible for all primes. More generally, it is conjectured that the p-adic Galois representations associated to cuspidal automorphic representations of GL(n) should always be irreducible.
Title: Local root numbers for Heisenberg representations
Abstract: On the Langlands program, explicit computation of the local root numbers (or epsilon factors) for Galois representations is an integral part. But for arbitrary Galois representation of higher dimension, we do not have explicit formula for local root numbers. In our recent work (joint with Ernst-Wilhelm Zink) we consider Heisenberg representation (i.e., it represents commutators by scalar matrices) of the Weil
Cohomology jump loci are secondary cohomological invariants of discrete groups and topological spaces. I will describe some recent work on the cohomology jump loci of complements of unions of smooth complex hypersurfaces, and I will motivate the notion of abelian duality spaces that I introduced in joint work with Alex Suciu and Sergey Yuzvinsky. The study of such hypersurface arrangements involves a mix of combinatorics and complex geometry.
Abstract: I will discuss two stochastic target problem in the Brownian framework .
The first problem has a nice solution which I will present. The second problem
is much more complicated and for now remains open. I will discuss the challenges and connection with other fields in probability theory.
Abstract: In this talk I will show that for finite entropy countable Markov shifts the entropy map is upper semi-continuous when restricted to the set of ergodic measures. This is joint work with Mike Todd and Anibal Velozo.
Title: Chang's Conjecture (joint with Monroe Eskew)
Abstract:
I will review some consistency results related to Chang's Conjecture (CC).
First I will discuss some classical results of deriving instances of CC from huge cardinals and the new results for getting instances of CC from supercompact cardinals, and present some open problems.
Then, I will review the consistency proof of some versions of the Global Chang's Conjecture - which is the consistency of the occurrence many instances of CC simultaneously.
We will aim to show the consistency of the statement: (\mu^+,\mu) -->> (
u^+,
