## Colloquium of the Department of Mathematics and Statistics

Starting on January 28, 2009, a Colloquium of the Department of Mathematics and Statistics will convene once a month during the semesters. The Colloquium will convene on the last Wednesday of each month from 16:15 to 17:00.

Each colloquium talk will be given in English by a distinguished mathematician/statistician/computer scientist either from our own department or by a guest.

Department Colloquium

Wednesday, April 17, 2019 in the Auditorium CK112 at 4.15pm.

Speaker: University lecturer Ritva Hurri-Syrjänen

University of Helsinki

Title: On Sobolev-type inequalities and beyond

Department Colloquium

Wednesday, December 19, 2018 in the Auditorium CK112 at 4.15 PM.

Speaker: Associate Professor Jani Virtanen

University of Reading

Title: Toeplitz determinants and their applications in mathematical physics

Department Colloquium

Wednesday, November 28, 2018 in the Auditorium CK112 at 4.15 PM.

Speaker: Professor Agnieszka Kalamajska

University of Warsaw and Polish Academy of Sciences

Title: Strongly nonlinear multiplicative inequalities

Department Colloquium

Wednesday, October 31, 2018 in the Exactum Auditorium CK 112at 4.15 PM.

Speaker: Lecturer Tuomas Sahlsten

University of Manchester

Title: How to find a criminal from a city of millions?

Department Colloquium

### Wednesday, September 26, 2018 at 4.15 PM in the Exactum Auditorium CK 112.

Speaker: Senior Lecturer Petteri Harjulehto

University of Turku

Title: Generalized Orlicz spaces and related variational problems

The fourth and last Departmental Colloquium (laitoskollokvio) of the fall term

will take place on

### Wednesday, December 14, in the Auditorium CK112 at 4.15 PM.

Speaker:

University Lecturer Jari Taskinen

University of Helsinki

WHEELTAPPERS, COMPACT SETS AND SOBOLEV EMBEDDINGS

Abstract:

In linear algebra we learn that given a self-adjoint nxn-matrix

A one can find an orthonormal basis of the n-dimensional Euclidean space,

which consists of eigenvectors of A. The concepts of eigenvalues and

eigenvectors generalize to spectral theory of linear operators in Hilbert

spaces. Two reasons make this a fundamental object of study. First, it is

a beautiful, nontrivial abstract mathematical theory. Second, very many

linearized physical models are based on it. In particular the propagation

of acoustic (or many other types of) waves in a given domain \Omega

depends on the spectral problem for the underlying elliptic partial

differential equation (PDE).

The functional analytic approach to elliptic PDE's involves Sobolev-Hilbert

spaces and Sobolev embedding theorems. We sketch this classical approach

and review recent research (jointly with S.A. Nazarov), emphasizing the

interesting phenomena created by geometrically nontrivial domains \Omega.

As is already a custom, after the talk there will be wine, pizza,

and beverages available. Everyone is warmly welcome!

The third Departmental Colloquium (laitoskollokvio) of the fall term will take place on

### Wednesday, November 30, in the Auditorium CK112 at 4.15 PM.

Speaker:

Professor Mika Seppälä, Helsinki

University of Helsinki and Florida State University

Algebraic Curves, Riemann Surfaces, and their Jacobians

Abstract:

Compact Riemann surfaces, projective algebraic curves, and their Jacobian varieties are different views of the same object. Classical methods make this result explicit in the case of genus one Riemann surfaces. To find a method to pass numerically from a given Riemann surface to a representation of the same object as an algebraic curve, and then to compute approximations of its Jacobian, is a difficult open problem in the general case. The main obstacle here is Hilbert’s 22nd problem, the problem of numerical uniformization. This can be solved in the case of hyper-elliptic algebraic curves using a method of P. J. Myrberg.

As is already a custom, after the talk there will be wine, pizza,

and beverages available. Everyone is warmly welcome!

The second Departmental Colloquium (laitoskollokvio) of the fall term will take place on

### Wednesday, October 26, in the Auditorium A111 at 4.15 PM.

Speaker: Professor Gunther Uhlmann

University of Washington (Seattle)

Title and abstract will be given later.

The first Departmental Colloquium (laitoskollokvio) of the fall term will take place on

### Wednesday, September 28, in the Auditorium CK112 at 4.15 PM.

Speaker: Professor Tom Körner

Cambridge University

Title: Why is Analysis 101 so hard?

As is already a custom, after the talk there will be wine, pizza,

and beverages available. Everyone is warmly welcome!

The abstract of the talk is below.

Best regards, Pertti Mattila

Abstract:

It is very hard to prove things that we know are true.

By studying analysis over the rationals rather than the

reals it becomes clear that the things we think are necessarily

true are not. I shall give simple examples, known to

all professionals, and a couple of examples which

may be less known.

The Departmental Colloquium (laitoskollokvio) of May will take place on

### Wednesday, May 25, in the Auditorium CK112 at 4.15 PM.

Speaker: Professor Gaven J. Martin

Massey University, New Zealand

Title: Quasiregular Mappings, Curvature & Dynamics.

The abstract of the talk is below.

Best regards, Matti Lassas

Abstract:

We survey recent developments in the area of geometric function theory and nonlinear analysis and in particular those that pertain to recent developments linking these areas to dynamics and rigidity theory in higher dimensions. A self mapping of an n-manifold is rational or uniformly quasiregular if it preserves some bounded measurable conformal structure. Because of Rickman's version of Montel's theorem there is a close analogy between the dynamics of rational mappings of closed manifolds and the classical Fatou-Julia theory of iteration of rational mappings of the complex plane. The theory is particularly interesting on the Riemann n-sphere where many classical results find their analogue. We also present recent results toward classifying manifolds admitting rational maps.

**The talk has a broad mix of different mathematics and is intended for a general audience.**

The Departmental Colloquium (laitoskollokvio) of April will take place on

### Wednesday, April 27, in the Auditorium CK112 at 4.15 PM.

Speaker: Professor Pentti Saikkonen, University of Helsinki

Title: Parameter Estimation in Nonlinear Autoregressive Models with Generalized Autoregressive Conditional Heteroskedasticity.

The abstract of the talk is below.

Best regards, Matti Lassas

Abstract: Parameter estimation in nonlinear autoregressive (AR) models with the conditional variance specified as a general nonlinear first order generalized autoregressive conditional heteroskedasticity (GARCH(1,1)) model is discussed. Such models are widely used to analyze financial time series in fields such as economics, finance, and insurance. The focus of the talk is in some special issues encountered in establishing strong consistency and asymptotic normality of the Gaussian quasi maximum likelihood (QML) estimator.

The Departmental Colloquium (laitoskollokvio) of March will take place on

### Wednesday, March 30, in the Auditorium CK112 at 4.15 PM.

Speaker: Professor Kari Astala

University of Helsinki

Title: Holomorphic motions

and beverages available. Everyone is warmly welcome!

The abstract of the talk is below.

Best regards, Matti Lassas

Abstract:

What happens when the space is deformed so that the time-dependence is complex analytic

(holomorphic) ? Briefly: What if time is holomorphic ?

Such questions arise in complex dynamics, Kleinian groups and geometric analysis, giving

rise to the notion of holomorphic motions. These then give, for instance,

a natural explanation of the geometric stability in dynamical systems.

We review first few of the surprising properties of holomorphic motions and their

relations to analysis and geometry.

The Departmental Colloquium (laitoskollokvio) of February will take place on

### Wednesday, February 23, in the Auditorium CK112 at 4.15 PM.

Speaker: Professor Jouko Väänänen

University of Helsinki

Title: Logic and set theory

and beverages available. Everyone is warmly welcome!

The abstract of the talk is below.

Best regards, Matti Lassas

Abstract:

Abstract: I will give a quick glimpse of mathematical logic from the vantage point of set theoretic model theory, focusing on two particular problems, one related to generalized quantifiers and another related to infinitary logic.

The first Departmental Colloquium (laitoskollokvio) of the spring term will take place on

### Wednesday, January 26, in the Auditorium CK112 at 4.15 PM.

Speaker: Professor Peter Lindqvist

Norwegian University of Science and Technology, Trondheim

Title: The Infinity-Laplace Equation

and beverages available. Everyone is warmly welcome!

The abstract of the talk is below.

Best regards, Matti Lassas

Abstract:

The Infinity-Laplace Equation is akin to the ubiquitous Laplace Equation and it has been intensively studied during the last 15 years. This "fully non-linear equation" has connexions to several branches of mathematics: calculus of variations, partial differential equations, probability theory , image processing, and so on.

Its solutions, the infinity-harmonic functions, provide the optimal Lipschitz-extension of the boundary values. The modern concept of viscosity solutions, originally created for first order equations by Lions, Evans, Ishii, Jensen, and others, plays a central role. --The connexion to game theory is spectacular, a game ("Tug-of-War") replacing the Brownian motion.

The talk is about this fascinating equation, once called "the Last Great Scalar Equation" by Evans.

The last Departmental Colloquium (laitoskollokvio) of the fall term will take place

### Wednesday, December 15, in the Auditorium CK112 at 4.15 PM.

Speaker: Professor Kari Vilonen (Northwestern University)

Title: The microlocal codimension three conjecture

Abstract below.

As is already a custom, after the talk there will be wine, pizza and beverages available! ... and don't forget that the chairman (MG) of the department wants everyone to be present.

Jouko Väänänen

Czar of the Colloquium

Abstract:

According to an old well-established principle, special functions (or distributions) can be understood and analyzed in terms of the systems of differential equations that they satisfy. To this end, a general theory of systems of linear (micro) differential equations was developed by the Sato school in Kyoto. This point of view, in its various incarnations, is now ubiquitous in many parts of mathematics allowing functions to be replaced by geometric objects. In joint work with Kashiwara we have proved the main longstanding conjecture in this subject, the codimension three conjecture. I will explain this conjecture and some of the very general ideas which enter the proof.

The next Departmental Colloquium (laitoskollokvio) of the fall term will take place

### Wednesday, November 24, in the Auditorium CK112 at 4.15 PM.

Speaker: Professor Antti Kupiainen.

Title: Renormalization - from Magic to Mathematics.

Abstract below.

As is already a custom, after the talk there will be wine, pizza and beverages available! ... and don't forget that the chairman (MG) of the department wants everyone to be present.

Jouko Väänänen

Czar of the Colloquium

Abstract:

Renormalization Group emerged half a century ago to deal with the problem of divergencies physicists encountered when trying to do calculations in Quantum Electrodynamics. Subsequently it developed into a powerful tool to deal with multi scale problems both in physics and mathematics.

We review these developments and explain some more recent applications of Renormalization Group to probability.

The next Departmental Colloquium (laitoskollokvio) of the fall term will take place

### Wednesday, October 27, in the Auditorium CK112 at 4.15 PM.

The speaker is Professor Michael Lacey (Georgia Institute of Technology).

Title: Pointwise Convergence of Fourier Series: Past, Present and Future.

Abstract below.

As is already a custom, after the talk there will be wine, pizza and beverages available! ... and don't forget that the chairman (MG) of the department wants everyone to be present.

Jouko Väänänen

Czar of the Colloquium

Abstract:

We recall Lennart Carleson's Theorem asserting the pointwise convergence of partial summation of Fourier series of square integrable functions. We explain what the Theorem says, and why it is worthy of citation by the Abel Prize committee: It is a "multi-scale" theorem. The talk finishes with related results that suggest possibilities for 'non-commutative' variants of Carleson's Theorem.

The next Departmental Colloquium (laitoskollokvio) of the fall term will take place at the expected time:

### Wednesday, September 29, in the Auditorium CK112 at 4.15 PM.

The speaker is Professor Jukka Corander.

Title: Have I Seen You Before? Principles of predictive classification revisited.

Abstract below.

As is already the custom, after the talk there will be wine, pizza and beverages available! ... and don't forget that the chairman (MG) of the department wants everyone to be present.

Jouko Väänänen

Czar of the Colloquium

Abstract: Classification of objects into a finite set of alternative classes based on observed features of the objects is a common task in statistical machine learning. An important application example familiar to most of us is spam filtering of email messages. In this talk we review the probabilistic basis of generative classification and show how a particular inductive rule of classification arises from basic principles of predictive probabilistic modeling pioneered by Seymour Geisser in 1960's. The standard practice of classifying objects one by one, which follows from an i.i.d. assumption, is demonstrated to be at odds with laws of predictive probability and we show also that it can be motivated as an asymptotic approximation to a more coherent rule. A novel inductive principle of predictive classification is introduced and we discuss its properties in relation to other principles.

The first Departmental Colloquium (laitoskollokvio) of the fall term will take place

### Wednesday, September 15, in the Auditorium CK112 at 4.15 PM.

The speaker is Professor Menachem Magidor (Hebrew University, Jerusalem).

Title: Some reflections on the Continuum Hypothesis.

Abstract below.

Jouko Väänänen

Czar of the Colloquium

Abstract:

The continuum problem is the problem of determining whether the cardinality of the real line is the immediate successor of the cardinality of the integers or there is a set of reals whose cardinality is strictly between the cardinality of the integers and the reals. The Continuum Problem was the first problem on Hilbert’s famous list. The problem turned out to be undecidable by the usual axiom systems for Set Theory. The results of Gödel and Cohen tell us that the axioms give very little information about the relative size of the set of integers and the set of reals. Gödel’s conjecture that strong axioms of infinity will settle the problem turned out to be false. Is this the end of the story?

In this talk we shall survey some of the current approaches of trying to give a meaningful answer to the problem, in spite of its independence. Two direction of research we shall concentrate on will be forcing axioms and the theory of universally Baire sets of reals.

The fourth colloquium of the spring term will take place

### Wednesday, April 28, in the Auditorium CK112 at 4.15 PM.

The speaker is: Professor Eero Saksman

Title: On random geometry

Abstract: An emerging new field, vaguely called 'Random Geometry', is described through some examples. The case of random conformal welding

is considered in more detail.

... and don't forget that the chairman (MG) of the department wants everyone to be

present.

The third colloquium of the spring term will take place

### Wednesday, March 31, in the Auditorium CK112 at 4.15 PM.

The speaker is: Professor Jean Bricmont (Université catholique de Louvain)

Title: From the microscopic to the macroscopic world.

Abstract: Basic physics studies microscopic equations, i.e. Newton's or Schödinger's

equations. But another part of physics, as well as most applications, deals with

macroscopic equations, such as the heat, Navier-Stokes or Boltzmann equations. Are the

latter independent of the microscopic equations? Are they rather a consequence of them?

Does the derivation of the macroscopic equations from the microscopic ones involve some

new principle? Part of the problem is that the microscopic equations describe the world

in the same way whether we go from past to future or from future to past, while the

macroscopic equations do not: they are compatible with the increase of entropy (or the

second law of thermodynamics) and have therefore an intrinsic time direction.

The goal of the talk will be to sketch an answer to those questions for a mathematical

audience.

... and don't forget that the chairman (MG) of the department wants everyone to be

present.

The second colloquium of the spring term will take place

### Wednesday, February 24, in the Auditorium CK112 at 4.15 PM.

The speaker is:

Professor Karen Smith (University of Michigan + University of Jyväskylä)

Title: "Thresholds of Singularities."

Abstract:

Consider a polynomial function f on complex N space. We say that f is singular at a point if its gradient vanishes there. But how can we quantify how singular? I will present three different ways of trying to quantify or measure the singularities of a polynomial or analytic function. The most classical involves using integration to measure how fast the reciprocal approaches infinity at the singular points. Or using algebraic geometry, we can measure the singularities in terms of the complicatedness of a "resolution of singularities". Finally, we can also "reduce mod p" and study the behavior of f under the Frobenius (or p-th power) map. Amazingly, all these different ways of measuring singularities turn out to be more or less equivalent, and I hope to hint at why.

beverages available! ... and don't forget that the chairman (MG) of

the department wants everyone to be present.

Yours Sincerely,

Kari Astala

Czar of the Colloquium

The first colloquium of the spring term will take place

### Wednesday January 27, in the Auditorium CK112 at 4.15 PM.

The speaker is:

Professor Juha Kinnunen (Helsinki University of Technology - Aalto University)

Title: On a theorem of Beckenbach and Rado for subharmonic functions.

Abstract: Beckenbach and Rado characterized logarithmically subharmonic functions in the plane in terms of integral inequalities involving spherical averages. We extend this result to higher dimensions and thus answer a question raised by Beckenbach and Rado. We also consider related integral inequalities suggested by Beckenbach and Rado and discuss connections to Muckenhoupt's weights.

As is already a custom, after the talk there will be wine, pizza and beverages available! ... and don't forget that the chairman (MG) of

the department wants everyone to be present.

Yours Sincerely,

Kari Astala

Czar of the Colloquium

The colloquium in December will take place

### Wednesday, December 9:th, 2009, in the Auditorium CK112 at 4.15 PM.

The speaker is UNIVERSITY LECTURER TAPANI HYTTINEN, and he will give a talk on

FINDING FIELDS

#### Abstract

Suppose a (large) blackboard is equipped with tools that allow one to draw a line

through any given two distinct points, draw the common point of any two intersecting lines

and draw a line which contains a given point and is parallel with a given line.

Then given three distinct points, call them 0, 1 and I, which are not collinear,

it is elementary to construct using these tools an addition and a multiplication to the

set of points of the line containing 0 and 1 so that it becomes isomorphic with the field of real numbers. In the talk I will look at variations of this construction,

some old and some more recent.

As is already a custom, after the talk there will be wine, pizza and beverages available! ... and don't forget that the chairman of the department wants everyone to be present.

### Previous colloquia

### Wednesday, November 25, 2009, in the Auditorium CK112 at 4.15 PM.

The speaker is PROFESSOR MAARIT JÄRVENPÄÄ, and he will give a talk on

HOW TO TURN A NEEDLE?

#### Abstract

In 1917 S. Kakeya asked the following question nowadays known as the Kakeya needle problem: what is the least amount of

area required to rotate continuously a unit line segment in the plane by a full rotation? I discuss the history and some

recent developments related to this problem.

As is already a custom, after the talk there will be wine, pizza and beverages available! ... and don't forget that the chairman of the department wants everyone to be present.

### Previous colloquia

### Wednesday, October 28, 2009, in the Auditorium CK112 at 4.15 PM.

The speaker is PROFESSOR JANI ONNINEN, and he will give a talk on

DEFORMATIONS OF FINITE (TOTAL) CONFORMAL ENERGY AND THE NITSCHE CONJECTURE

#### Abstract

We give an account of a few of recent developments in which the quasiconformal

theory and nonlinear elasticity share common problems of compelling mathematical

interest. We study deformations between bounded domains in Euclidean n-space. There are

many new and unexpected phenomena concerning existence, uniqueness and failure of radial

symmetry of the extremal deformations. We also introduce natural conditions on the

integrand that guarantee the existence and global invertibility of the minimizers. The

talk is based on joint work with Tadeusz Iwaniec and Leonid V. Kovalev.

As is already a custom, after the talk there will be wine, pizza and beverages available! ... and don't forget that the chairman of the department wants everyone to be present.

### Wednesday, September 30, 2009, the Auditorium CK112 at 4.15 PM.

The speaker is PROFESSOR MATTI JUTILA, and he will give a talk on

THE ROLE OF HARDY'S FUNCTION IN THE THEORY OF RIEMANN'S ZETA FUNCTION

#### Abstract

The following topics will be discussed: the history of Riemann's zeta-function with its connection to the distribution of primes,

definition and basic properties of Hardy's function, its role in the characterization and numerical verification of Riemann's hypothesis,

and recent work on the integral function of Hardy's function.

### Wednesday, June 3., 2009, the Auditorium CK112 at 4.15 PM.

The speaker is PROFESSOR MATS GYLLENBERG and he will give a talk on

POPULATION DYNAMICS, DELAY EQUATIONS AND SEMIGROUPS

#### Abstract

In this talk I explain the basic principles for modelling structured populations. I show that every relevant population model could and should be formulated as a delay equation. Finally I show how the theory of adjoint semigroups can be used for stability and bifurcation analysis of delay equations.

### Wednesday, April 29, 2009, the Auditorium CK112 at 4.15 PM.

The speaker is PROFESSOR JOUKO MICKELSSON, and he will give a talk on

THE GOOD, THE BAD AND THE UGLY: THE OPERATOR RESIDUE, THE TRACE, AND THE FREDHOLM INDEX

#### Abstract

Index theory of Fredholm operators lies at the crossroads of analysis, geometry, and topology with important applications to mathematical physics. The great breakthrough in the geometric index theory was made in seminal papers by M.F. Atiyah and I.M. Singer about fourty years ago, and since then there has been active research on this field with new connections to other fields of mathematics and physics.

In this talk I want to describe in a simple manner some aspects of the theory using a method based on residue calculus and trace extensions of linear operators in a Hilbert space.

### Wednesday, March 25, 2009, in the Auditorium CK112 at 4.15 PM.

The speaker is PROFESSOR YUVAL PERES, Microsoft research and University of Washington, and he will give a talk on

VISUAL MATHEMATICS- THE CASE OF FAIR ALLOCATIONS

#### Abstract

I will give some recent examples where properly simulating and viewing mathematical objects has led to new mathematics, some of it appearing in the Annals of Math.

I will focus on the fair allocation problem: Given an infinite collection of points in the plane (a point process) how do we allocate the same area to each point in a decentralized way? See http://www.stat.berkeley.edu/~peres/stable/stable.htmlfor one solution, and http://depts.washington.edu/probab/research.php for another.

Different approaches to this problem have connections with probability, combinatorics, ergodic theory, the Riemann mapping theorem, and Newtonian gravity (in higher dimensions); see the gallery at http://www.math.huji.ac.il/~romik/Site/Allocations.html but there is lots of room for new creative ideas.

The talk will be accessible to a broad mathematical audience.

### Wednesday, February 25, 2009, the Auditorium CK112 at 4 PM.

The speaker is professor PROFESSOR SAMULI SILTANEN and he will give a talk on

INVERSION METHODS FOR THREE-DIMENSIONAL MEDICAL X-RAY IMAGING

#### Abstract

In medical X-ray tomography, three dimensional structure of tissue is reconstructed from a collection of projection images.

Mathematically, this data can be interpreted as a collection of line integrals of nonnegative X-ray attenuation coefficient. In many practical imaging situations only a small number of truncated projections is available from a limited range of view.

Traditional reconstruction algorithms, such as filtered backprojection, do not give satisfactory results when applied to such

data. More suitable reconstruction algorithms based on Bayesian inversion are studied. In this approach, a priori information is used to compensate for the incomplete information of the measurement data. Examples with in vitro measurements from dental radiology are presented.

After the talk there will be wine and pizza!

### Wednesday, January 28, 2009, the Auditorium CK112

The speaker is PROFESSOR ELJA ARJAS and he will give a talk on

RANDOMNESS, PROBABILITY, AND LEARNING:

SOME SIMPLE ILLUSTRATIONS AND IDEAS,

#### Abstract:

The purpose of this talk is to discuss first principles of statistical inference in the context of simple random sampling. In particular, I will consider the situation of data accumulating over time, and the consequent learning. The only prerequisite for following the talk is familiarity with the basic rules of probability calculus.

NOTE ALSO THAT WINE WILL BE SERVED AFTER THE COLLOQUIUM.