Seminars and Colloquia by Series

Monday, April 1, 2019 - 12:50 , Location: Skiles 005 , TBA by Maria Angelica Cueto , Ohio State University , , Organizer: Yoav Len
Monday, April 1, 2019 - 12:45 , Location: Skiles 006 , Ahmad Issa , University of Texas, Austin , Organizer: Jennifer Hom
Monday, April 1, 2019 - 11:15 , Location: Skiles 005 , Ben Webb , BYU , , Organizer:
<p>One of the characteristics observed in real networks is that, as a network's topology evolves so does the network's ability to perform various complex tasks. To explain this, it has also been observed that as a network grows certain subnetworks begin to specialize the function(s) they perform. We introduce a model of network growth based on this notion of specialization and show that as a network is specialized its topology becomes increasingly modular, hierarchical, and sparser, each of which are properties observed in real networks. This model is also highly flexible in that a network can be specialized over any subset of its components. By selecting these components in various ways we find that a network's topology acquires some of the most well-known properties of real networks including the small-world property, disassortativity, power-law like degree distributions and clustering coefficients. This growth model also maintains the basic spectral properties of a network, i.e. the eigenvalues and eigenvectors associated with the network's adjacency network. This allows us in turn to show that a network maintains certain dynamic properties as the network's topology becomes increasingly complex due to specialization.</p>
Monday, April 1, 2019 - 11:00 , Location: Skiles 005 , Ben Webb , BYU , , Organizer:
Saturday, March 30, 2019 - 14:00 , Location: Atlanta , Georgia Tech Tropical Arithmetic and Combinatorial Algebraic-geometry , Georgia Institute of Technology , Organizer: Yoav Len

This is a two day conference (March 30-31) to be held at Georgia Tech on algebraic geometry and related areas. We will have talks by Sam Payne, Eric Larson, Angelica Cueto, Rohini Ramadas, and Jennifer Balakrishnan. See for more information.

Friday, March 29, 2019 - 15:05 , Location: Skiles 005 , Yinon Spinka , University of British Columbia, Vancouver, Canada , Organizer: Prasad Tetali
Thursday, March 28, 2019 - 15:05 , Location: Skiles 006 , Liza Rebova , Mathematics, UCLA , Organizer: Christian Houdre
Thursday, March 28, 2019 - 15:00 , Location: Skiles 005 , Fan Wei , Stanford University , Organizer: Xingxing Yu
Reed and Wood and independently Norine, Seymour, Thomas, and Wollan showed that for each $t$ there is $c(t)$ such that every graph on $n$ vertices with no $K_t$&nbsp;minor&nbsp;has at most $c(t)n$&nbsp;cliques. Wood asked in 2007 if $c(t)<c^t$ for some absolute constant $c$. This problem was recently solved by Lee and Oum. In this paper, we determine the exponential constant. We prove that every graph on $n$ vertices with no $K_t$&nbsp;minor&nbsp;has at most $3^{2t/3+o(t)}n$&nbsp;cliques. This bound is tight for $n \geq 4t/3$. We use the similiar idea to give an upper bound on the number of&nbsp;cliques&nbsp;in an $n$-vertex graph with no $K_t$-subdivsion. Easy computation will give an upper bound of $2^{3t+o(t)}n$; a more careful examination gives an upper bound of $2^{1.48t+o(t)}n$. We conjecture that the optimal exponential constant is $3^{2/3}$ as in the case of&nbsp;minors. This is a joint work with Jacob Fox.
Thursday, March 28, 2019 - 11:00 , Location: Skiles 006 , Eugenia Malinnikova , Norwegian University of Science and Technology , Organizer: Mayya Zhilova
The Remez inequality for polynomials quantifies the way the maximum of a polynomial over an interval is controlled by its maximum over a subset of positive measure. The coefficient in the inequality depends on the degree of the polynomial; the result also holds in higher dimensions. We give a version of the Remez inequality for solutions of second order linear elliptic PDEs and their gradients. In this context, the degree of a polynomial is replaced by the Almgren frequency of a solution. We discuss other results on quantitative unique continuation for solutions of elliptic PDEs and their gradients and give some applications for the estimates of eigenfunctions for the Laplace-Beltrami operator. The talk is based on a joint work with A. Logunov.
Wednesday, March 27, 2019 - 15:00 , Location: Skiles 006 , Liza Rebrova , UCLA , , Organizer: Galyna Livshyts