Colloquium of the Department of Mathematics and Statistics

 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 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

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, 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 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 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.

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.

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.

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.

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.

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 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.

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.

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.

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, 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.

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.

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.

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, 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.

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, 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.