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Combinatorics and geometry of hyperbolic and stable polynomials

4-5 November 2015

Mini-course (organiser: Oleg Pikhurko)

Petter Brändén (KTH Stochholm)

Combinatorics and geometry of hyperbolic and stable polynomials

Over the past decade there has been several successful applications of the geometry of zeros of hyperbolic and stable polynomials to problems in combinatorics, computer science, probability theory, convex optimisation and other areas of mathematics. For example, simple proofs of generalisations of the van der Waerden conjecture, a theory of negative dependence in probability theory, a theory around the Lee-Yang program on phase transitions in statistical mechanics, a proof of the existence of families of bipartite Ramanujan graphs of every degree, the solution to the Kadison-Singer problem, and progress on the traveling salesman problem.

In these lectures we will survey on the theory around stable and hyperbolic polynomials, as well as showing how these techniques can applied to problems in the areas mentioned above.

Schedule

4th Nov
9:00-11:00 Long lecture in B1.01
11:00-11:15 Coffee in the Common Room followed by discussions
12:00 Lunch in the Common Room

5th Nov
9:00-10:00 Lecture in MS.04
10:00-10:30 Coffee in the Common Room followed by discussions
12:00 Lunch in the Common Room
13:00-14:00 Lecture in MS.04

Please register here.

Also, Petter will talk about "Non-representable hyperbolic matroids" at the combinatorics seminar 2-3pm on 6 November (Friday).

The mini-course is funded by the European Research Council and Warwick's Mathematics Institute.

Aerial photograph of Maths Houses

See also:
Mathematics Research Centre
Mathematical Interdisciplinary Research at Warwick (MIR@W)
Past Events 
Past Symposia 

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Contact:
Mathematics Research Centre
Zeeman Building
University of Warwick
Coventry CV4 7AL - UK
E-mail:
mrc@maths.warwick.ac.uk