## 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.

Welcome to the Departmental Colloquium on

**Wednesday 25th of March at 4.15 pm in Exactum lecture hall CK112 **

The speaker will be

** Professor Spyridon Alexakis (University of Toronto)**

He is going to speak about:

**"The impossibility of periodic motion in general relativity."**

As usual, pizza and drinks will be served after the colloquium.

Welcome to the Departmental Colloquium on

**Wednesday 1st of October at 4 pm in Exactum lecture hall CK112 **

The speaker will be

** Johan Stén (VTT)**

He is going to speak about:

**Anders Johan Lexell - a Finnish comet of the Enlightenment**

As usual, pizza and drinks will be served after the colloquium.

Welcome to the Departmental Colloquium on

**Wednesday 28 May at 16:15 in A111 in Exactum **

The speaker will be

** Heikki Haario, Professor of mathematics at Lappeenranta University of Technology**

He is going to speak about:

**On uncertainty quantification of weather and climate models**

As usual, pizza and drinks will be served after the colloquium.

Welcome to the Departmental Colloquium on

**Wednesday 26 March at 16:15 in CK112 in Exactum (usual time and place)!**

The speaker will be

** Camilla Hollanti, Assistant professor of mathematics at Aalto University**

She is going to speak about:

**Algebraic Number Theory meets Wireless Communications**

Abstract:

In wireless communications the transmitted signals are prone to errors caused by fading and noise. To combat fading, so-called space-time codes can be utilized. During the past ten years, there has been a continuous race to improve the performance of MIMO space-time codes by means of algebraic number theory. In this talk, I will give an overview on the MIMO communication problem and space-time codes, and survey some results related to algebraic number theory.

Short bio

Camilla Hollanti is an assistant professor at Aalto University School of Science. She got her PhD from the University of Turku in 2009, and her research interests include algebra, number theory, and applications to wireless communications.

As usual, pizza and drinks will be served after the colloquium.

Welcome to the Departmental Colloquium on

**Wednesday 26 February at 16:15 in CK112 in Exactum (usual time and place)!**

The speaker will be

** Erik Aurell, Professor of biological physics at KTH - Royal Institute of Technology**

He is going to speak about:

**Inference for large-scale Potts models using pseudolikelihood**

Abstract:

The large majority of cellular functions are executed and controlled by the coordinated action of thousands of proteins the biological

functions of which are strongly connected to their three-dimensional (3D) structure. Despite many years of intensive work in the field, and many

partial successes, predicting the 3D structure of one protein from its amino acid sequence alone is a major unsolved problem of biophysics

and computational biology.

As a by-product of the sequencing revolution the number of sequenced proteins (the amino acid sequence of which is known) is however

today much larger, and grows much more quickly, than the number of known protein structures. Over the last five years very significant

progress has accordingly been made by leveraging the statistical information in a set of homologous (similar) protein sequences.

I will review this progress in the field with an emphasis on our own work based on a learning a probabilistic model from data by

maximizing a pseudo-likelihood function.

Short bio

Erik Aurell is Professor of Biological Physics at KTH-Royal Institute of Technology, Stockholm, Sweden, since 2003. He was Finland Distinguished Professor 2008-2013 and is since January 1 2014 Aalto University Adjunct Professor. His research interests include statistical physics, computational biology and, recently, statistical inference. He is a co-PI of Finnish Center of Excellence in Computational Inference.

As usual, pizza and drinks will be served after the colloquium.

Welcome to the Departmental Colloquium on

**Wednesday 29 January at 16:15 in CK112 in Exactum (usual time and place)!**

The speaker will be

** Teemu Roos, Assistant Professor of Computer Science at our own university**

He is going to speak about:

**Complexity in Statistical Inference**

Abstract:

In this talk, I will explore to which extent a 'rule of simplicity' can be applied in statistical modeling. This will take us on a tour in information theory, where simplicity and its opposite, complexity, are measured in terms of entropy, data compression, and computability. We will discuss the modern version of Occam's razor, known as the Minimum Description Length (MDL) Principle, and relate it to more classical statistical concepts as well as Bayesian methods.

Short bio

Teemu Roos is an Assistant Professor at the Department of Computer Science, University of Helsinki, Finland. He received a Ph.D. degree in 2007 from the same University. Before his present position, Teemu has held postdoctoral and other academic visiting positions at University of California, Berkeley, MIT, and University of Cambridge. He is a member of Finnish Center of Excellence in Computational Inference. His research interests include machine learning, data analysis, and information theory.

As usual, pizza and drinks will be served after the colloquium.

Welcome to the Departmental Colloquium on

**Wednesday 27 November at 16:15 in CK112 in Exactum (usual time and place)!**

The speaker will be

**Juha Alho, Professor of Social Statistics at our own university**

He is going to speak about:

**How Long can We Live? Statistical Perspectives on Longevity**

Abstract:

Historical evidence supports the view that life expectancy did not systematically increase for centuries before the 1800's. After that, there has been a sustained increase. The increase has repeatedly been assumed to stop in the foreseeable future. This assumption has not been based on empirical evidence, and it has lead to major underestimates in forecasts of the elderly population. The uncertainty of future evolution of longevity can be characterized using statistical modeling. This is illustrated via the life expectancy adjustment factor of pension level. Such an adjustment is currently in use in Finland and Sweden, for example.

As usual, pizza and drinks will be served after the colloquium.

Welcome to the autumn's second Departmental Colloquium on

**Wednesday 30 October at 16:15 in CK112 in Exactum (usual time and place)!**

The speaker will be

**Valtteri Niemi, Professor at the University of Turku**

Dr. Niemi is a cryptographer who has made a long career at Nokia Research Center before taking his current position. His talk will be on the following topic:

Title:

**Classes of garbling schemes**

Abstract:

The history of garbled circuits traces back to Andrew Yao, who introduced the technique in 1980s. The term "garbled circuit" was introduced by Beaver, Micali and Rogaway for the purpose of performing secure multiparty computation with Yao’s circuit garbling technique. Since then Yao’s garbled circuits have been used for various purposes even though it was not formally defined what is meant by garbling.

Recently, Bellare, Hoang and Rogaway elevated garbled circuits from a cryptographic technique to a cryptographic goal by defining several new security notions for garbled circuits. This talk explains these fundamental notions, motivation behind them and basic results. Then we continue by extending some of the results and providing both new notions and new results about various classes of garbling schemes.

As usual, pizza and drinks will be served after the colloquium.

Welcome to the autumn's first Departmental Colloquium on

**Wednesday 25 September at 16:15 in CK112 in Exactum (usual time and place)!**

The speaker will be

**Dr. Tuomo Kuusi, Academy Research Fellow from Aalto University**

Title:

**Potential estimates and nonlinear partial differential equations**

Abstract:

I will give an update to some aspects of the theory for solutions to nonlinear, possibly degenerate Poisson equations involving p-Laplace type operators. The datum, in full generality, can be a measure. We have obtained in a nonlinear fashion a series of new pointwise potential estimates for solutions to these equations and the main focus of the talk is to describe them. The foundation of the representation will be our recent survey article.

As usual, pizza and drinks will be served after the colloquium.

### May Colloquium: On Wednesday, May 29, 4:15pm

Place: Room CK112 in Exactum

Kimmo Uutela (GE Healthcare Finland) will speak about

"Mathematics in patient monitoring "

April Colloquium: On Wednesday, April 24, 4.15pm

Place: Room CK112 in Exactum

Juha Oikkonen (University of Helsinki) will speak about

"A nowhere differentiable continuous function: some mathematical thinking and thoughts about mathematical thinking "

### March Colloquium: On Wednesday, March 27, 4.15pm

Place: Room CK112 in Exactum

Distinguished Professor Tadeusz Iwaniec (University of Helsinki) will speak about

" Sobolev Mappings and Energy Integrals in Geometric Function Theory and Nonlinear Elasticity "

### February Colloquium: On Wednesday, February 20, 4.15pm

Place: Room CK112 in Exactum

Per Christian Hansen (Technical University of Denmark) will speak about

"IMAGE DEBLURRING WITH KRYLOV SUBSPACE METHODS"

Abstract:

Image deblurring, i.e., reconstruction of a sharper image from a blurred and noisy one, involves the solution of a large and very ill-conditioned

system of linear equations, and regularization is needed in order to compute a stable solution. Krylov subspace methods are often ideally suited

for this task: their iterative nature is a natural way to handle such large-scale problems, and the underlying Krylov subspace provides a convenient

mechanism to regularized the problem by projecting it onto a low-dimensional "signal subspace" adapted to the particular problem. In this talk we

consider the three Krylov subspace methods CGLS, MINRES, and GMRES. We describe their regularizing properties, and we discuss some

computational aspects such as preconditioning and stopping criteria.

**January Colloquium: On Wednesday, January 30, 4:15pm**

Place: Room CK112 in Exactum

Andres Villaveces ( National University of Colombia ) will speak about

"MODEL THEORY, BECOMING MORE GEOMETRIC?"

Abstract:

Some recent (and some not so recent) interaction is taking place at the crossroads between Logic (more specifically, Model Theory) and Geometry

(including sheaves and schemes, operator algebras and their associated geometric treatment, even some number theoretic situations).

I will illustrate some of the places where this interaction happens and illustrate some of the lines of work that are being opened right now.

### November Colloquium: On Wednesday, November 28, 4.15pm

Place: Room CK112 in Exactum

Jean-Pierre Eckmann (University of Geneva) will speak about

"ATOMS, NUCLEI AND 3D TRIANGULATIONS"

Abstract:

How many ways are there to make topological triangulations with n triangles, with t tetrahedra?

For triangles, this problem has been solved (exactly!) long ago. For tetrahedra, the answer is unknown.

I will revisit this question and explain some ideas of Durhuus-Jonsson and Benedetti-Ziegler.

I introduce a notion of nucleus (a triangulation of the 3-ball without internal nodes, and with each internal face having at most 1 external edge).

I show that every triangulation can be built from trees of nuclei.

This leads to a new reformulation of Gromov's question: I show that if the number of rooted nuclei with t

tetrahedra is exponentially bounded in t, then the number of rooted triangulations with t tetrahedra is also exponentially bounded.

This is joint work with Pierre Collet and Maher Younan.

### October Colloquium: On Wednesday, October 31, 4.15pm

Place: Room CK112 in Exactum

Professor Kaisa Matomäki (Turku University) will speak about

"Additive problems involving primes"

Abstract:

In the first part of the talk I will introduce and discuss two additive problems involving primes: Goldbach's conjecture (every even number greater than two is the sum of two primes) and occurrence of primes in arithmetic progressions. In the second part I will talk about these two problems for positive density subsets of the primes.

### September Colloquium: On Wednesday, September 26, 4.15pm

Place: Room CK112 in Exactum

Professor Alexander Engström (Aalto University) will speak about

"Polytopes from subgraph statistics"

Abstract:

Exponential random graph models are used by statisticians to understand local and global behaviour of large networks. This is applied to model for example how people interact in societies and the Internet. To find the right random model, one needs to understand polytopes of subgraph statistics. A complete understanding of those polytopes would kill several areas of combinatorics and computer science, so it might not be attainable. With Patrik Norén I've looked at how to approximate them with semi-algebraic sets. Along the road we found several surprising results, like a version of Selberg's integral formula to calculate some volumes. I will mostly show pictures of graphs, polytopes, their approximations, and try to connect the dots.

### May Colloquium: On Wednesday 4.15pm, May 23

Place: Room CK112 in Exactum

Professor Peter Jones (Yale University) will speak about

"Product Formulas for Measures and Applications to Analysis and Geometry"

Abstract: We will discuss product formulas for positive measures and give three applications:

1. Study of network traffic. (Joint work with D. Bassu, L. Ness, V. Rokhlin)

2. Constructions of random curves. (Joint work with K. Astala, A. Kupiainen, E. Saksman)

3. Geometry of Lebesgue measurable sets and differentiablity of Lipschitz functions. (Joint work with M. Csörnyei)

Most of the time will be spent on topic 3. The starting point is elementary product formalisms for positive measures, due to R. Fefferman, C. Kenig, and J. Pipher. We will give some background where there have been previous applications to analysis and geometry. The new result in topic 3 concerns Lebesgue measurable sets E of small Lebesgue measure (in any dimension). The set E can be decomposed into a bounded number of sets with the property that each (sub)set has a nice "tangent cone". Roughly speaking each subset has very small intersection with any Lipschitz curve whose tangent vector (to that curve) always lies inside a fixed cone. This had been proven in dimension two by Alberti, Csörnyei, and Preiss by using special, two dimensional combinatorial arguments. The main technical result needed in our work is a d dimensional, measure theoretic version of (a geometric form of) the Erdös-Szekeres theorem. (The discrete form of E-S is known only in d = 2.) In what is perhaps a small surprise, certain ideas from random measures can be used effectively in the deterministic setting. Our result yields strong results on Lipschitz functions: For any Lebesgue null set E in d dimensions, there is a Lipshitz mapping of Euclidean d space to itself, that is nowhere differentiable on E. (Thus Rademacher's theorem, which states that such a map is a.e. differentiable, is sharp. Any Lebesgue null set can be in the set of non-differentiability for such a Lipschitz function.)

After the colloquium there will be served some beverages, snacks, and wine.

Everybody is warmly welcome!

### Colloquium in April: On Wednesday 4.15pm, April 25

Place: Room CK112

Professor Jukka Corander will speak about

"How has our understanding about bacterial evolution evolved during the

genomic era?"

Abstract:

Bacteria were originally considered to be asexually reproducing

organisms, however, as early as 1927, the seminal experiment performed

by Fred Griffith revealed a mechanism of horizontal transfer by which

bacteria can integrate new functionalities to their genomes by re-using

pieces of DNA from their environment. Later also other important

mechanisms of horizontal gene transfer have been discovered and studied

in detail. Nevertheless, it is only very recently we have been able to

investigate the role of these mechanisms in the evolution on a larger

scale when advances in sequencing technology made it possible to analyze

large sets of whole genomes for closely related samples from a bacterial

population. In the talk I will explain Griffith's experiment and the

mathematical basis of modelling evolutionary processes and the genetic

structure of bacterial populations in absence and presence of horizontal

transfers. In general, the data sets emerging in near future pose an

astronomic modelling challenge since inference must be done in the

presence of billions of parameters. Results from our recent projects

will be used to illustrate the central concepts.

After the talk there will be wine, pizza,

and beverages available. Everyone is warmly welcome!

### The March Colloquium of the Department of Mathematics and Statistics will take place

on Wednesday 4.15pm, March 28

Place: Room CK112

Assoc. prof. Tuomas Hytönen will give a talk with the title

"How much, or little, is necessary for (harmonic) analysis?"

Abstract:

One aspect of my recent work has been developing harmonic analysis

under minimal

assumptions on the space on which the considered functions are

defined. Perhaps

surprisingly, some classical methods, which at first sight seem to

rely heavily on the structure and symmetries of the Euclidean space,

can actually be extended to very general settings. On the other hand,

some methods developed to tackle with abstract spaces, have shown to

be instrumental for getting sharp results for classical inequalities

on the Euclidean space.

After the talk there will be wine, pizza,

and beverages available. Everyone is warmly welcome!

### The February Colloquium of the Department of Mathematics and Statistics will take place

on Wednesday 4.15 pm, 29th of February.

Place: Room CK112

Dr Esko Keski-Vakkuri http://www.helsinki.fi/~keskivak/

will speak about

"D-branes and dualities"

The theory of D-branes was a breakthrough development in string theory

in 1995.

Since then they have in different ways been a cornucopia of new results in

quantum field theory, string theory and many branches of mathematics. One

of the reasons for this is that they give remarkable relations (dualities)

between theories of fundamental matter and spacetime geometry.

I will try to give an introduction to what D-branes are, and what kind of

relations to lead to. Time permitting, as an example of recent

research I may discuss quantum entanglement as geometry of minimal

surfaces in pseudo-Riemannian manifolds.

After the talk there will be wine, pizza,

and beverages available. Everyone is warmly welcome!

### The first colloquium of 2012 of the Department of Mathematics and Statistics will take place

on Wednesday 4.15 pm, 25th of January.

Place: CK112

The speaker is

Professor Matti Lassas, University of Helsinki

Title:

Cloaking, Invisibility, and Inverse Problems

Abstract:

We describe recent theoretical and experimental progress on making objects

invisible to detection by electromagnetic waves, acoustic waves and quantum

waves. For the case of electromagnetic waves, Maxwell's equations have

transformation laws that allow the design of electromagnetic materials that

steer waves having a given frequency around a hidden region, returning it to

its original path on the far side. Not only would observers be unaware of the

contents of the hidden region, they would not even be aware that something

was being hidden. An object, located in the hidden region, is said to be

cloaked.

In the talk, we concentrate on the mathematical theory of invisibility

cloaking involving inverse problems, differential geometry, and the degenerate

differential equations.

Same procedure as every time: After the talk there will be wine, pizza,

and beverages available. Everyone is warmly welcome!

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.