Wed, February 8, 2017
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February 2017
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11:00am [11:00am] R. V. Gurjar
Title: Rational Singularities VI

[11:00am] Srikanth Srinivasan
Title: Recent developments on the Sunflower conjecture Abstract: A sunflower with p petals is a family of sets A_1,...,A_p such that the intersections of all pairs of distinct sets are the same. A famous conjecture in combinatorics, called the Sunflower conjecture, asserts a bound on the maximum size of any family of k-sets that does not contain a p-sunflower. We review some recent work by Ellenberg-Gijswijt and Naslund-Swain that proves a weak variant of this conjecture due to Erdos and Szemeredi.

4:00pm [4:00pm] Math Colloquium
Speaker: Willem H. Haemers Tilburg University, The Netherlands Title: Are almost all graphs determined by their spectrum? Abstract: An important class of problems in mathematics deals with the reconstruction of a structure from the eigenvalues of an associated matrix. The most famous such prob- lem is: ‘Can one hear the shape of a drum?’. Here we deal with the question: ‘Which graphs are determined by the spectrum (eigenvalues) of its adjacency matrix’? More in particular we ask ourselves whether this is the case for almost all graphs. There is no consensus on what the answer should be, although there is a growing number of experts that expect it to be affirmative. In this talk we will present several re- sults related to this question. This includes constructions of cospectral graphs and characterizations of graphs by their spectrum. Some of these results support an affirmative answer, some support the contrary. It will be explained why the speaker believes that it is true.