Events - Department of Mathematics

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The Department of Mathematics is a bustling place full of new ideas. We host several events that occur throughout the year, including seminars, colloquium, conferences, and social events. Our seminars and colloquium are open to the public: all students, faculty, or alumni who are interested are welcome to join us for exciting talks on the leading edge of mathematics research!

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Graph Theory and Combinatorics Seminar: Almost k-Covers of Grids

Event Type
Jan 18, 2022   1:00 pm  
Alexander Clifton

Alon and Furedi determined the minimum number of affine hyperplanes needed to cover all but one vertex of an $n$-cube. We extend this question to the case where all vertices must be covered at least k times, except for one which is not covered at all. Using the Punctured Combinatorial Nullstellensatz of Ball and Serra, we solve the problem completely for $k=3$ and establish a nontrivial lower bound when k>3. Time permitting, we will also discuss this problem for more general grids, including an exact solution for k=2.

Joint work with Hao Huang.

For Zoom information, please contact Sean at SEnglish (at) illinois (dot) edu

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