Seminars and Colloquia by Series

Monday, April 1, 2019 - 12:50 , Location: Skiles 005 , TBA by Maria Angelica Cueto , Ohio State University , cueto.5@osu.edu , Organizer: Yoav Len
TBA
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 , bwebb@math.byu.edu , 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 , bwebb@math.byu.edu , 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 https://sites.google.com/view/gattaca/home 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 , rebrova@math.ucla.edu , Organizer: Galyna Livshyts
TBA

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