Seminars and Colloquia by Series

Series: PDE Seminar
Thursday, April 26, 2018 - 15:00 , Location: Skiles 257 , Alberto Maspero , SISSA , alberto.maspero@sissa.it , Organizer: Yao Yao
We prove an abstract theorem giving a $t^\epsilon$ bound for any $\epsilon> 0$ on the growth of the Sobolev norms in some abstract linear Schrödinger equations. The abstract theorem is applied to  nonresonant Harmonic oscillators in R^d. The proof is obtained by conjugating the system to some normal form in which the perturbation is a smoothing operator. Finally, time permitting, we will show how to construct a perturbation of the harmonic oscillator which provokes growth of Sobolev norms.
Monday, April 23, 2018 - 15:00 , Location: Skyles006 , Amnon Besser , Georgia Tech/Ben-Gurion University , amnon.besser@gmail.com , Organizer:
The talk reports on joint work with Wayne Raskind and concerns the conjectural definition of a new type of regulator map into a quotient of an algebraic torus by a discrete subgroup, that should fit in "refined" Beilinson type conjectures, exteding special cases considered by Gross and Mazur-Tate.The construction applies to a smooth complete variety over a p-adic field K which has totally degenerate reduction, a technical term roughly saying that cycles acount for the entire etale cohomology of each component of the special fiber. The regulator is constructed out of the l-adic regulators for all primes l simulateously. I will explain the construction, the special case of the Tate elliptic curve where the regulator on cycles is the identity map, and the case of K_2 of Mumford curves, where the regulator turns out to be a map constructed by Pal. Time permitting I will also say something about the relation with syntomic regulators.
Monday, April 23, 2018 - 14:00 , Location: Skiles 006 , Hong Van Le , Institute of Mathematics CAS, Praha, Czech Republic , hvle@math.cas.cz , Organizer: Thang Le
Novikov  homology was introduced by  Novikov in  the early 1980s motivated by problems  in hydrodynamics.  The Novikov inequalities in the Novikov homology theory give lower bounds for the number of critical points of a Morse  closed 1-form  on a compact  differentiable manifold M. In the first part of my talk  I shall survey  the Novikov homology theory in finite dimensional setting and its  further developments  in infinite dimensional setting with applications in the theory of symplectic fixed points and Lagrangian intersection/embedding problems. In the  second part of my talk I shall report  on my recent joint work with Jean-Francois Barraud  and Agnes Gadbled on construction  of the Novikov fundamental group  associated to a  cohomology class  of a closed 1-form  on M  and its application to obtaining  new lower bounds for the number of critical points of  a Morse 1-form.
Friday, April 20, 2018 - 15:05 , Location: Skiles 271 , Prof. Rafael de la Llave , GT Math , Organizer: Jiaqi Yang
A well known paper of H. Federer on Flat chains contains a remarkable example attributed  to F. Almgren. We intend to give a geometric exposition of the example and explain its relevance in the global theory of geodesic flows and some global problems such as homogenization in quasi-periodic media. This is part of an expository paper with X. Su.
Friday, April 20, 2018 - 15:05 , Location: Skiles 271 , Prof. Rafael de la Llave , GT Math , Organizer: Jiaqi Yang
A well known paper of H. Federer on Flat chains contains a remarkable example attributed  to F. Almgren. We intend to give a geometric exposition of the example and explain its relevance in the global theory of geodesic flows and some global problems such as homogenization in quasi-periodic media. This is part of an expository paper with X. Su.
Friday, April 20, 2018 - 13:05 , Location: Skiles 005 , Kira Goldner , CSE, University of Washington , kgoldner@cs.washington.edu , Organizer: He Guo
Consider the problem of selling items to a unit-demand buyer. Most work on maximizing seller revenue considers either a setting that is single dimensional, such as where the items are identical, or multi-dimensional, where the items are heterogeneous. With respect to revenue-optimal mechanisms, these settings sit at extreme ends of a spectrum: from simple and fully characterized (single-dimensional) to complex and nebulous (multi-dimensional). In this paper, we identify a setting that sits in between these extremes. We consider a seller who has three services {A,B,C} for sale to a single buyer with a value v and an interest G from {A,B,C}, and there is a known partial ordering over the services. For example, suppose the seller is selling {internet}, {internet, phone}, and {internet, cable tv}. A buyer with interest {internet} would be satisfied by receiving phone or cable tv in addition, but a customer whose interest is {internet, phone} cannot be satisfied by any other option. Thus this corresponds to a partial-ordering where {internet} > {internet, phone} and {internet} > {internet, cable tv}, but {internet, phone} and {internet, cable tv} are not comparable. We show formally that partially-ordered items lie in a space of their own, in between identical and heterogeneous items: there exist distributions over (value, interest) pairs for three partially-ordered items such that the menu complexity of the optimal mechanism is unbounded, yet for all distributions there exists an optimal mechanism of finite menu complexity. So this setting is vastly more complex than identical items (where the menu complexity is one), or even “totally-ordered” items as in the FedEx Problem [FGKK16] (where the menu complexity is at most seven, for three items), yet drastically more structured than heterogeneous items (where the menu complexity can be uncountable [DDT15]). We achieve this result by proving a characterization of the class of best duals and by giving a primal recovery algorithm which obtains the optimal mechanism. In addition, we (1) extend our lower-bound to the Multi-Unit Pricing setting, (2) give a tighter and deterministic characterization of the optimal mechanism when the buyer’s distribution satisfies the declining marginal revenue condition, and (3) prove a master theorem that allows us to reason about duals instead of distributions. Joint work with Nikhil Devanur, Raghuvansh Saxena, Ariel Schvartzman, and Matt Weinberg.
Friday, April 20, 2018 - 10:00 , Location: Skiles 006 , Jose Acevedo , Georgia Tech , Organizer: Kisun Lee
In this talk we show how to obtain some (sometimes sharp) inequalities between subgraph densities which are valid asymptotically on any sequence of finite simple graphs with an increasing number of vertices. In order to do this we codify a simple graph with its edge monomial and establish a nice graphical notation that will allow us to play around with these densities.  
Thursday, April 19, 2018 - 15:05 , Location: Skiles 006 , Tomasz Tkocz , Carnegie Mellon University , ttkocz@math.cmu.edu , Organizer: Michael Damron
 We shall prove that a certain stochastic ordering defined in terms of convex symmetric sets is inherited by sums of independent symmetric random vectors. Joint work with W. Bednorz.
Thursday, April 19, 2018 - 13:30 , Location: Skiles 005 , Alexander Hoyer , Math, GT , Organizer: Robin Thomas
Györi and Lovasz independently proved that a k-connected graph can be partitioned into k subgraphs, with each subgraph connected, containing a prescribed vertex, and with a prescribed vertex count. Lovasz used topological methods, while Györi found a purely graph theoretical approach. Chen et al. later generalized the topological proof to graphs with weighted vertices, where the subgraphs have prescribed weight sum rather than vertex count. The weighted result was recently proven using Györi's approach by Chandran et al. We will use the Györi approach to generalize the weighted result slightly further. Joint work with Robin Thomas.
Wednesday, April 18, 2018 - 14:10 , Location: Skiles 006 , Sarah Davis , GaTech , Organizer: Anubhav Mukherjee
The theorem of Dehn-Nielsen-Baer says the extended mapping class group is isomorphic to the outer automorphism group of the fundamental group of a surface. This theorem is a beautiful example of the interconnection between purely topological and purely algebraic concepts. This talk will discuss the background of the theorem and give a sketch of the proof.

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