Wed, February 1, 2017
Public Access Category: All |
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- Time:
- 11:00am-12:00pm
- Location:
- Ramanujan Hall
- Description:
- Title: The Capset bound of Croot-Lev-Pach and Ellenberg-Gijswijt
Abstract: A construction of Behrend from the 1940s shows that there are subsets of [N] of size N^{1-o(1)} that contain no 3-term APs (also called capsets). For a long time, it was open whether there is such a construction over F_3^n (i.e. a capset in F_3^n of size 3^{n-o(n)}). Recently, building on work of Croot, Lev and Pach, it was shown by Ellenberg and Gijswijit ( https://arxiv.org/abs/1605.09223 ) that such a construction does not exist: i.e. any capset in F_3^n can have size at most c^n for some c < 3. The construction has had several applications already in Combinatorics and Theoretical Computer Science. We will see a proof of the theorem of Ellenberg and Gijswijt
- Time:
- 11:30am
- Location:
- Room No. 216
- Description:
- Title. Rational Surface Singularities.
Title. We will prove a purely numerical criterion due to M. Artin to test
the rationality of a surface singularity. In practice this is the
criterion which is used when a rational surface singularity is being
considered.
- Time:
- 2:30pm-3:30pm
- Location:
- Ramanujan Hall
- Description:
- Title: Existence and regularity theory in weighted Sobolev spaces and
applications.
Abstract: My emphasis in this talk will be on functional analytical tools to
the solvability and uniqueness of solutions to the nonhomogeneous boundary
value problems, dealing with degenerate PDEs of elliptic type. My aim is to
consider possibly general class of weights. In particular, I consider the
$B_{p}$-class of weights, introduced by Kufner and Opic, which is much more
general class than the commonly studied Muckenhoupt $A_{p}$-class.