Mathematics

Discrete Geometry and Combinatorics Seminar

Spring 2017

All seminars (unless otherwise stated) will take place on Tuesdays at 5.00pm in Room 707 (25 Gordon Street). See the map for further details. There will be tea afterwards in Mathematics Room 606 (25 Gordon Street). If you require any more information on the Applied seminars please contact Dr John Talbot (e-mail: j.talbot AT ucl.ac.uk or tel: 020-7679-4102).

23 January 2018

Speaker: David Ellis (QMUL)

Title: Symmetric Intersecting Families of Sets


Abstract:
Let X be a finite set. We say a family F of subsets of X is 'three-wise intersecting' if any three sets in F have nonempty intersection; we say it is 'symmetric' if it has transitive automorphism group. Frankl conjectured in 1981 that if F is a symmetric, three-wise intersecting family of subsets of an n-element set, then F has size o(2^n). We will discuss a recent (and surprisingly short) proof of this conjecture. Joint work with Bhargav Narayanan (Rutgers).

30 January 2018

Speaker: Samuel Porritt (UCL)

Title: Irreducible polynomials over F_q with restricted coefficients


Abstract:
In 2010 Mauduit and Rivat proved that, asymptotically, there are the same number of primes with an even as with an odd number of digits when written in binary (and similar results for other bases). In 2016 Maynard proved an asymptotic formula for the number of primes less than X which can be written in a given base with certain digits not used. We will discuss analogues of these two results for polynomials over a finite field. As in the integer setting, the proofs are based on the circle method but are much simpler thanks to strong estimates for exponential sums over irreducible polynomials and some technical simplifications due to the fact that we don’t “carry digits” when adding polynomials over a finite field.