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**Discrete Geometry and Combinatorics Seminar**- Previous Discrete Geometry and Combinatorics Seminars
- Discrete Geometry and Combinatorics Seminar Autumn 2017
- Discrete Geometry and Combinatorics Seminar Summer 2017
- Discrete Geometry and Combinatorics Seminar Spring 2017
- Discrete Geometry and Combinatorics Seminar Autumn 2016
- Discrete Geometry and Combinatorics Seminar Summer 2016
- Discrete Geometry and Combinatorics Seminar Spring 2016
- Discrete Geometry and Combinatorics Seminar Autumn 2015
- Discrete Geometry and Combinatorics Seminar Summer 2015
- Discrete Geometry and Combinatorics Seminar Spring 2015
- Discrete Geometry and Combinatorics Seminar Autumn 2014
- Discrete Geometry and Combinatorics Seminar Summer 2014
- Discrete Geometry and Combinatorics Seminar Spring 2014
- Discrete Geometry and Combinatorics Seminar Autumn 2013
- Discrete Geometry and Combinatorics Seminar Spring 2013
- Discrete Geometry and Combinatorics Seminar Autumn 2012
- Discrete Geometry and Combinatorics Seminar Spring 2012
- Discrete Geometry and Combinatorics Seminar Autumn 2011
- Discrete Geometry and Combinatorics Seminar Spring 2011
- Discrete Geometry and Combinatorics Seminar Autumn 2010
- Discrete Geometry and Combinatorics Seminar Spring 2010
- Discrete Geometry and Combinatorics Seminar Autumn 2009
- Discrete Geometry and Combinatorics Seminar Spring 2009

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## Discrete Geometry and Combinatorics Seminar

### Spring 2018

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.

### 27 February 2018

#### Speaker: Prof William Jackson (QMUL)

###### Title: Unique low rank completability of partially filled matrices

**Abstract:**

I will consider the matrix completion problem
- we are given a partially filled matrix and want to add entries in such a
way that the resulting matrix has low rank. More precisely, I will assume that
such a completion exists and ask whether it is unique. I will also consider the
variants when the completed matrix should have the additional properties that
it is a gram matrix or is skew-symmetric. I will describe how techniques from
rigidity theory can be applied to help analyse these problems.

### 06 March 2018

#### Speaker: Peter Komjath, Eotvos University (Budapest)

###### Title: Geometric constructions in the Euclidean spaces requiring the Axiom of Choice

**Abstract:**

We present some results on
Euclidean spaces
whose proof require the Axiom of choice.
An example is: the plane is the union of
countably many
parts, none containing two distinct points which
span
rational distance. One can see that some of the
parts
must be Lebesgue nonmeasurable, so no easily
definable
decomposition work.

We will mention results of R. O. Davies, P.
Erdos, and
J. Schmerl.