Thursday, October 25, 2018
Time  Items 

All day 

10am 
10/25/2018  10:20am We will present a geometric representation theory proof of a mild version of the BeauvilleVoisin conjecture for Hilbert schemes of K3 surfaces, namely the injectivity of the cycle map on the subring of Chow generated by tautological classes. To this end, we lift formulas of Lehn and LiQinWang from cohomology to Chow groups, and use them to quickly solve the problem by invoking the irreducibility criteria of Virasoro algebra modules. Joint work with Davesh Maulik. Location:
LOM 200

3pm 
10/25/2018  3:00pm Milnor fibers are invariants that arise in the study of hypersurface singularities. A major open conjecture predicts that for hyperplane arrangements, the Betti numbers of the Milnor fiber depend only on the combinatorics of the arrangement. I will discuss how tropical geometry can be used to study related invariants, the virtual Hodge numbers of a hyperplane arrangement’s Milnor fiber. This talk is based on joint work with Max Kutler. Location:
LOM 202

4pm 
10/25/2018  4:00pm A classical result of Mantel states that every graph of density larger than 1/2 contains a triangle, and this result is best possible. In this talk, we study two Mantelinspired problems: the first one asks what is the minimum $d$ such that any triple of graphs $G_1, G_2, G_3$ on the same vertexset all of density larger than d contains a transversal triangle, i.e., three edges $uv,vw,wu$ in $G_1,G_2,G_3$, respectively. We show that $d = (52  4\sqrt{7}) / 81$ suffices, which is asymptotically best possible witnessed by a construction discovered by Aharoni and DeVos. Moreover, their construction is asymptotically the only extremal configuration. The second problem, which is due to DeVos, McDonald and Montejano, states that every $k$edgecolored graph where each color class has density more than $1/(2k1)$ contains a nonmonochromatic triangle. This talk is based on joint works with E. Culver, B. Lidicky, F. Pfender and S. Norin. Location:
DL 431
10/25/2018  4:15pm Varieties of general type, CalabiYau varieties and Fano varieties are building blocks of varieties in the sense of birational geometry. It is expected that such varieties satisfy certain finiteness. Birkar recently proved that Fano varieties with bounded singularities belong to finitely many algebraic families (BAB Conjecture). We show that rationally connected klt CalabiYau 3folds form a birationally bounded family. This is a joint work with W. Chen, G. Di Cerbo, C. Jiang, and R. Svaldi. Location:
LOM 214
