Uppsala Ph.D. Mathematics Conference

Friday 6 Mar 2020, 08:45 → 20:00 Europe/Stockholm

4001 (Ångströmslaboratoriet)

The department of mathematics at Uppsala University welcomes Ph.D. students in the field of mathematics to a one-day conference. All students from any field of mathematics are welcome. The primary audience is students from the greater Stockholm-Uppsala region, for whom some financial support had been made available by way of the department paying for tickets.

By bringing together students in the area the conference hopes to establish and foster connections between researchers at the beginning of their careers.

The preliminary list of speakers is:

• Daniel Ahlsen (Stockholm University)
• Eric Ahlqvist (KTH)
• Johan Asplund (Uppsala University)
• Martina Favero (KTH)
• Lukas Kristiansson Schoug (KTH)
• Johanna Strömberg (Uppsala University)

Maps

• Map_ChinaGarden_Dinner.png
• Map_Interior.png
• Map_Rullan_Lunch.png
• Map_Uppsala.png

08:45 → 09:15 Pickup from Centralstation

09:15 → 09:45 Fika

09:45 → 10:30 Ramified covers and root stacks

A ramified cover X of a surface S gives rise to ramification data in the following sense: the locus in S over which X is ramified will look like a union of curves and to each curve we associate the corresponding ramification index. Conversely, given a finite number of curves in S intersecting only transversely, and a positive integer for each curve, we may ask when such data comes from a ramified cover. We will explain how to give a criteria for when this is the case, using root stacks.

Speaker: Eric Ahlqvist (KTH)

10:30 → 10:45 Break

10:45 → 11:30 Introduction to homological mirror symmetry and the Fukaya category

Homological mirror symmetry is a deep mathematical conjecture
proposed by Maxim Kontsevich at the 1994 ICM in Zürich, and it is about
a certain relationship between the two mathematical areas of symplectic
geometry and algebraic geometry. More precisely, the conjecture states
that there is a derived equivalence between the so-called Fukaya
category in symplectic geometry, and the category of coherent sheaves
which is well-studied in the field of algebraic geometry. The conjecture
is an attempt at understanding mirror symmetry in string theory which is
well-known by physicists.

In this talk I will first go through history and origins of the
conjecture. After that, an introduction to symplectic geometry will be
given and the goal will be to give the audience a feeling of what the
Fukaya category is.

Speaker: Johan Asplund (Uppsala University)

11:30 → 13:00 Lunch

13:00 → 13:45 Strategic ability, information and memory

A typical game theoretic question is this: given some set of information and available memory, what conditions can an agent force? This talk will tackle the converse: given a class of conditions, what information and memory does an agent need to force the conditions? Specifically, I present the logic ATL for reasoning about strategic ability in a multi-agent settings, and show that for certain fragments of ATL, one can restrict the information available to agents without limiting their strategic abilities.

Speaker: Daniel Ahlsén (Stockholm University)

13:45 → 14:00 Break

14:00 → 14:45 Importance sampling and weak convergence in population genetics

Importance sampling algorithms are used in population genetics to estimate small probabilities of gene configurations. ​In order to prove the efficiency of these algorithms, it is necessary to determine the asymptotic behaviour of the sampling probabilities. As a first step in this direction, we show weak convergence for a sequence of coalescent processes and the corresponding mutation processes, as the sample size goes to infinity. Time is scaled and convergence of semigroups is proved. The limiting process consists of a deterministic part and of conditionally independent Poisson processes with varying intensity. This is a work in progress with H.Hult (KTH)​.

Speaker: Martina Favero (KTH)

14:45 → 15:15 Fika

15:15 → 16:00 The Gaussian free field: local sets and their dimensions

The two-dimensional Gaussian free field is the canonical model for a random surface and is important in many different areas of mathematics and physics. It is the two-dimensional time analog of Brownian motion and enjoys many similar properties, such as a certain domain Markov property and local sets, i.e., higher-dimensional versions of stopping times. In this talk, we introduce these notions, with the Brownian motion in mind, and discuss the properties of these random sets as well as briefly describe how to compute the dimensions of a certain class of local sets. The talk is based on joint work with Avelio Sepúlveda and Fredrik Viklund.

Speaker: Lukas Kristiansson Schoug (KTH)

16:00 → 16:15 Break

16:15 → 17:00 Percolation

Percolation studies the behaviour of clusters in random graphs. It has applications to modeling phenomena as diverse as magnetism, spread of infectious diseases, and the adaption of new technologies in society. This talk will give a brief overview of the theory of percolation, starting from the celebrated Harris-Kesten theorem on percolation in the square lattice in two dimensions. We will in particular consider tools used to study percolation in random geometric graphs and the configuration model. Finally, we will consider what new questions arise when we drop the independence requirement from the standard percolation process.

Speaker: Johanna Strömberg (Uppsala University)

17:30 → 19:30 Dinner