# Forthcoming Seminars

Please note that the list below only shows forthcoming events, which may not include regular events that have not yet been entered for the forthcoming term. Please see the past events page for a list of all seminar series that the department has on offer.

Past events in this seriesGiven a log Calabi-Yau surface Y with maximal boundary D, I'll explain how to construct a mirror Landau-Ginzburg model, and sketch a proof of homological mirror symmetry for these pairs when (Y,D) is distinguished within its deformation class (this is mirror to an exact manifold). I'll explain how to relate this to the total space of the SYZ fibration predicted by Gross--Hacking--Keel, and, time permitting, explain ties with earlier work of Auroux--Katzarkov--Orlov and Abouzaid. Joint work with Paul Hacking.

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Please note that this seminar starts from 3:20.

TBA

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In some ways the theory of mapping class groups of 4-manifolds is in 2020 at the same place where the theory of mapping class groups of 2-manifolds was in 1973, before Thurston changed everything. In this talk I will describe some first steps in an ongoing joint project with Eduard Looijenga where we are trying to understand mapping class groups of certain algebraic surfaces (e.g. rational elliptic surfaces, and also K3 surfaces) from the Thurstonian point of view.

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## Further Information:

URL;[Meeting URL removed for security reasons]

We study dynamic backward problems, with the computation of conditional expectations as a special objective, in a framework where the (forward) state process satisfies a Volterra type SDE, with fractional Brownian motion as a typical example. Such processes are neither Markov processes nor semimartingales, and most notably, they feature a certain time inconsistency which makes any direct application of Markovian ideas, such as flow properties, impossible without passing to a path-dependent framework. Our main result is a functional Itô formula, extending the Functional Ito calculus to our more general framework. In particular, unlike in the Functional Ito calculus, where one needs only to consider stopped paths, here we need to concatenate the observed path up to the current time with a certain smooth observable curve derived from the distribution of the future paths. We then derive the path dependent PDEs for the backward problems. Finally, an application to option pricing and hedging in a financial market with rough volatility is presented.

Joint work with JianFeng Zhang (USC).

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Part of the Oxford Discrete Maths and Probability Seminar, held via Zoom. Please see the seminar website for details.

We say that a graph $G$ is $H$-free if $G$ does not contain $H$ as a (not necessarily induced) subgraph. For a positive integer $n$, denote by $\text{ex}(n,H)$ the largest number of edges in an $H$-free graph with $n$ vertices (the Turán number of $H$). The classical theorem of Erdős, Kleitman, and Rothschild states that, for every $r\geq3$, there are $2^{\text{ex}(n,H)+o(n2)}$ many $K_r$-free graphs with vertex set $\{1,…, n\}$. There exist (at least) three different derivations of this estimate in the literature: an inductive argument based on the Kővári-Sós-Turán theorem (and its generalisation to hypergraphs due to Erdős), a proof based on Szemerédi's regularity lemma, and an argument based on the hypergraph container theorems. In this talk, we present yet another proof of this bound that exploits connections between entropy and independence. This argument is an adaptation of a method developed in a joint work with Gady Kozma, Tom Meyerovitch, and Ron Peled that studied random metric spaces.

## Further Information:

Part of the Oxford Discrete Maths and Probability Seminar, held via Zoom. Please see the seminar website for details.

Let $X_1, \ldots$ be i.i.d. copies of some real random variable $X$. For any $\varepsilon_2, \varepsilon_3, \ldots$ in $\{0,1\}$, a basic algorithm introduced by H.A. Simon yields a reinforced sequence $\hat{X}_1, \hat{X}_2, \ldots$ as follows. If $\varepsilon_n=0$, then $\hat{X}_n$ is a uniform random sample from $\hat{X}_1, …, \hat{X}_{n-1}$; otherwise $\hat{X}_n$ is a new independent copy of $X$. The purpose of this talk is to compare the scaling exponent of the usual random walk $S(n)=X_1 +\ldots + X_n$ with that of its step reinforced version $\hat{S}(n)=\hat{X}_1+\ldots + \hat{X}_n$. Depending on the tail of $X$ and on asymptotic behavior of the sequence $\varepsilon_j$, we show that step reinforcement may speed up the walk, or at the contrary slow it down, or also does not affect the scaling exponent at all. Our motivation partly stems from the study of random walks with memory, notably the so-called elephant random walk and its variations.

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