Department of

Mathematics


Seminar Calendar
for events the day of Tuesday, April 17, 2018.

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Tuesday, April 17, 2018

11:00 am in 345 Altgeld Hall,Tuesday, April 17, 2018

About Bredon motivic cohomology of a field

Mircea Voineagu

Abstract: We introduce Bredon motivic cohomology and show that complexes of equivariant equidimensional cycles compute this cohomology. We use this and other methods to identify the Bredon motivic cohomology of a field in weight 0 and 1 as well as the Bredon motivic cohomology of the field of complex numbers. This is a joint work with J. Heller and P.A. Ostvaer.

3:00 pm in 243 Altgeld Hall,Tuesday, April 17, 2018

The Degrees of Varieties

Jason McCullough (Iowa State University)

Abstract: Let $K$ be an algebraically closed field and let $V$ be a projective variety (reduced, irreducible, nondegenerate) embedded in $\mathbb{P}^n_K$. There are two notions of degree associated to $V$: (1) the degrees of the generators of the defining homogeneous ideal of $V$, and (2) the number of points of intersection between $V$ and a linear space of complementary dimension. In the plane these two notions agree, but in higher dimension there was a only the conjectured inequality $\mathrm{maxdeg}(P) \leq \deg(V(P))$ for a prime ideal $P$. Recent joint work with Irena Peeva produced counterexamples to this conjecture and the Eisenbud-Goto conjecture. However, using the recent solution to Stillman's Conjecture by Ananyan and Hochster, we show that there is a bound on the defining equaltions of any variety purely in terms of its degree. This is joint work with Caviglia, Chardin, Peeva, and Varbaro.

3:00 pm in 241 Altgeld Hall,Tuesday, April 17, 2018

The Erdős–Gallai theorem for cycles in hypergraphs

Ruth Luo (UIUC Math)

Abstract: The Erdős–Gallai theorem states that if a graph $G$ on $n$ vertices has no cycle of length $k$ or longer, then $e(G) \leq (k-1)(n-1)/2$. We present a hypergraph analogue of this theorem. A berge-cycle of length $\ell$ in an $r$-uniform hypergraph is a set of $\ell$ hyperedges $\{e_1, ..., e_\ell\}$ and $\ell$ vertices $\{v_1, ..., v_\ell\}$ such that hyperedge $e_i$ contains the vertices $v_i$ and $v_{i+1}$. We show that for $r \geq k+1$, if $H$ is an $r$-uniform hypergraph on $n$ vertices with no berge-cycle of length $k$ or longer, then $|H| \leq (k-1)(n-1)/r$. This is joint work with Alexandr Kostochka.

4:30 pm in Ballroom, Alice Campbell Alumni Center,Tuesday, April 17, 2018

Department Awards Ceremony