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14:30 Jozef Skokan (LSE) Combinatorial Theory Seminar Add to calendar L3
Strong Ramsey saturation for cycles
We call a graph $ H $ Ramsey-unsaturated if there is an edge in the complement of $ H $ such that the Ramsey number $ r(H) $ of $ H $ does not change upon adding it to $ H $. This notion was introduced by Balister, Lehel and Schelp who also showed that cycles (except for $ C_4 $) are Ramsey-unsaturated, and conjectured that, moreover, one may add any chord without changing the Ramsey number of the cycle $ C_n $, unless $ n $ is even and adding the chord creates an odd cycle. We prove this conjecture for large cycles by showing a stronger statement: If a graph $ H $ is obtained by adding a linear number of chords to a cycle $ C_n $, then $ r(H)=r(C_n) $, as long as the maximum degree of $ H $ is bounded, $ H $ is either bipartite (for even $ n $) or almost bipartite (for odd $ n $), and $ n $ is large. This motivates us to call cycles strongly Ramsey-unsaturated. Our proof uses the regularity method.
15:45 Timo Schurg (Bonn) Algebraic and Symplectic Geometry Seminar Add to calendar L3
From perfect obstruction theories to commutative differential graded algebras
A perfect obstruction theory for a commutative ring is a morphism from a perfect complex to the cotangent complex of the ring satisfying some further conditions. In this talk I will present work in progress on how to associate in a functorial manner commutative differential graded algebras to such a perfect obstruction theory. The key property of the differential graded algebra is that its zeroth homology is the ring equipped with the perfect obstruction theory. I will also indicate how the method introduced can be globalized to work on schemes without encountering gluing issues.
17:00 Dr. M. de Visscher (City) Algebra Seminar Add to calendar L2
On simple modules for the Brauer algebra
Wed, 23/05
10:15 		Samuel Isaacson (Boston University) OCCAM Wednesday Morning Event Add to calendar OCCAM Common Room (RI2.28)
Relationships between several particle-based stochastic reaction-diffusion models
Particle-based stochastic reaction-diffusion models have recently been used to study a number of problems in cell biology. These methods are of interest when both noise in the chemical reaction process and the explicit motion of molecules are important. Several different mathematical models have been used, some spatially-continuous and others lattice-based. In the former molecules usually move by Brownian Motion, and may react when approaching each other. For the latter molecules undergo continuous time random-walks, and usually react with fixed probabilities per unit time when located at the same lattice site. As motivation, we will begin with a brief discussion of the types of biological problems we are studying and how we have used stochastic reaction-diffusion models to gain insight into these systems. We will then introduce several of the stochastic reaction-diffusion models, including the spatially continuous Smoluchowski diffusion limited reaction model and the lattice-based reaction-diffusion master equation. Our work studying the rigorous relationships between these models will be presented. Time permitting, we may also discuss some of our efforts to develop improved numerical methods for solving several of the models.

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