# Colloquium

The Department of Mathematics and Systems Analysis organizes regular colloquia on topics in mathematics and systems analysis for a non-specialist audience. Informal discussion continues after the colloquium in the common room.

#### Spring semester 2018

**January**** 3****0th****, 15-16, hall ****D**** : Prof. ****Petteri Kaski** (Aalto Univeristy) :* "Proofs and computation" :*

A highly desirable property for a mathematical proof is that its correctness is easier to verify than it is to prepare the proof from scratch. One possibility to quantify such "ease of verification" is to view the tasks of preparing and verifying a proof from a computational perspective and in terms of the computational resources employed for a task. Indeed, such proof-system-based characterizations are in many ways fundamental to our current understanding of computational complexity and complexity classes such as P, NP, and beyond. This talk explores classical and recent work on proof systems for computational problems, including some of our own recent work involving proof systems that tolerate adversarial errors during proof preparation*.*

We apply a recent statistical algorithm, originally developed for parameter estimation of chaotic dynamical systems, to identify model parameters of reaction-diffusion systems by ensembles of Turing patterns created by unknown random initial values. The method is tested using the Fitzhugh-Nagumo model, a classical model of excitable media. It is shown that the approach is able to detect small but systematic structural changes of patterns, practically impossible to distinguish by naked eye.

The developments of statistical mechanics and of quantum field theory are among the major achievements of 20th century's science. In the second half of the century, these two subjects started to converge, resulting in some of the most remarkable successes of mathematical physics. At the heart of this convergence lies the conjecture that critical lattice models are connected, in the continuous limit, to conformally symmetric field theories. This conjecture has led to much insight into the nature of phase transitions and to beautiful formulae describing lattice models, which have remained unproven for decades.

In this talk, I will focus on the planar Ising model, perhaps the most studied lattice model, whose investigation has initiated much of the research in statistical mechanics. I will explain how, in the last ten years, we have developed tools to understand mathematically the emerging conformal symmetry of the model, and the connections with quantum field theory. This has led one to the proof of celebrated conjectures for the Ising correlations and for the description of the emerging random geometry. I will then explain how these tools have then yielded a rigorous formulation of the field theory describing this model, allowing one to make mathematical sense of the seminal ideas at the root of the subject of conformal field theory.

## Titles and abstracts of past colloquia

#### Fall semester 2017

- September 26th, 15-16, hall M1 : Prof. Daniele Boffi ( Università di Pavia, Aalto University ) :
*"Finite element approximation of resonant modes for the Maxwell cavity problem"*
- October 31st, 15-16, hall U1 : Prof. Lothar Nannen (TU Wien) :
*"Numerical methods for resonance problems in open systems"*
- November 28th, hall U1 : Prof. Kari Astala (Aalto University) :
*"Random tilings, variational problems and the Beltrami equation"*

#### Spring semester 2017

- January 31st, 15-16, hall U1 : Jarkko Kari (University of Turku) :
*"An Algebraic Geometric Approach to Multidimensional Symbolic Dynamics"*
- February 28th, 15-16, hall M1 : Eero Saksman (University of Helsinki) :
*"The Riemann zeta function meets Gaussian multiplicative chaos"*
- March 28th, 15-16, hall M1 : Christian Haase (Freie Universität Berlin) :
*"Finiteness Theorems for Lattice Polytopes"*
- April 25th, 15-16, hall M1 : Thomas Britz (UNSW Sydney) :
*"A Nice Proof of Wei's Duality Theorem"*
- May 2nd, 15-16, hall M1 : David Rios Insua (ICMAT-CSIC and Royal Academy of Sciences, Spain) :
*"Adversarial Risk Analysis: Concepts, Applications and Challenges"*

#### Fall semester 2016

Spring semester 2016

- January 26th, 15-16, hall M1:Prof. Davy Paindavei (Université Libre de Bruxelles) :
*Inference on the mode of weak directional signals: a Le Cam perspective on hypothesis testing near singularities*
- February 23rd, 15-16, hall M1: Prof. Jeffery M. Keisler (Aalto University, University of Massachusetts Boston) :
*A decision analytic modification to deal with uncertain targets in project management*
- March 31th, 15-16, hall M1 : Prof. René Scoof (Università di Roma “Tor Vergata”) :
*Lagrange's theorem for finite algebraic groups*
- April 26th, 15-16, hall M1 : Prof. Giuseppe Mingione (Università di Parma) :
*Some regularity problems in the calculus of variations*

#### Fall semester 2015

- September 29, 15-16, hall M1: Prof. Raimo P. Hämäläinen (Aalto University) :
*Behavioural operational research. *
- October 27, 15-16, hall U1: Prof. David Radnell (Aalto University) :
*Some new developments in quasiconformal Teichmueller theory.*
- November 24th, 15-16, hall U1: Ph.D Jukka Keränen (Aalto Univerisity) :
*Group Representations in Number Theory: An Introduction to the Langlands Program*

Spring semester 2015

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