## Visiting address

Ullevål StadionSognsveien 77B

0855 OSLO

Norway

Time and place:
Mar. 1, 2018 2:30 PM - 3:30 PM,
Gates of Eden, Sognsv. 77B

**Abstract:**

The Hodge conjecture is a major unsolved problem in mathematics which forms a subtle bridge between algebraic geometry, differential geometry and topology. Formulated by Hodge in his 1950 ICM address, it asks for a characterisation of the subvarieties of a projective variety in terms of the topology of that variety. Today the conjecture remains widely open, and it is one of the seven `Millenium problems' for which the Clay Institute offers a prize of one million dollars. In this talk I will give an basic introduction to the circle of ideas around the conjecture, focusing on specific examples, pictures and important special cases.

NB! Coffee/Tea/Biscuits from 14.00.

Time and place:
Feb. 1, 2018 2:30 PM - 3:30 PM,
Gates of Eden, Sognsv. 77B

**Abstract:**

If X is a compact metric space, then a measure on X is a linear, bounded and positive operator on the space of continuous functions on X. If f:X->Y is a continuous map between compact metric spaces, then by tautology we can pushforward any measure on X. Can we pullback a measure? No answer had been found in the literature.

In this talk I will explain why we cannot pullback a measure to a measure in general, even in the case where f is an isomorphism over a dense open subset of Y. On the other hand, I will show that if f is a finite covering over a dense open subset of Y, then we can pullback any measure on Y to a more general class of so-called positive strong submeasures. This is then applied to dynamics of meromorphic maps of compact Kahler manifolds. This general class of strong submeasures can also be used in the problem of intersection of hypersurfaces.

NB! Coffee/Tea/Biscuits from 14.00.

Time and place:
Nov. 30, 2017 2:30 PM - 3:30 PM,
Gates of Eden, Sognsv. 77B

NB! Coffee/Tea/Biscuits from 14.00.

Time and place:
Nov. 2, 2017 2:30 PM - 3:30 PM,
Gates of Eden, Sognsv. 77 B

Professor Emeritus **Erling Størmer** will turn 80 on November 2, and he will use this occasion to give a Colloquium Talk with tittle:

POSITIVE LINEAR MAPS ON MATRIX ALGEBRAS

*Abstract: The first part of the talk will be an introduction to the theory of positive linear maps between matrix algebras, plus a few words on the operator algebra case. For the last 20 years, physicists working in quantum information theory have been active in the subject and I’ll devote the last half of the talk to a negative solution to a conjecture they had. *

Time and place:
June 14, 2017 10:15 AM - 3:30 PM,
VB Aud 4 (Aud 5 fra kl. 13.30)

Den 14. juni 2017 er det 100 år siden Atle Selberg ble født. Han regnes som en av de fremste tallteoretikerne i verden gjennom tidene og mottok bl.a. Fieldsmedaljen i 1950 og Wolfprisen i 1986. Han hadde hele sin studietid ved UiO, der han tok doktorgraden i 1942.

Matematisk Institutt ved UiO vil markere jubileet på selve dagen den 14. juni.

Time and place:
May 18, 2017 2:30 PM - 3:30 PM,
Rest area 7. floor

*Abstract: I will discuss the two main syntheses that occured duing the "wavelet revolution" in the second half of the 1980s: one concerning the many aspects of what we now call wavelets, another concerning the relations between conjugate mirror filters, multiresolution approximations and orthonormal wavelet bases.*

Coffee/tea and cookies will be served from 14.00 to 14.30.

Time and place:
May 11, 2017 12:45 PM - 1:45 PM,
Abels utsikt 12. floor

Time and place:
May 5, 2017 12:45 PM - 1:45 PM,
Rest area 7. floor

Time and place:
Aug. 25, 2016 2:30 PM - 3:30 PM,
Rest area 7.floor NHA

Coffee/Tea/Biscuit from 14.00

Time and place:
May 20, 2016 2:30 PM - 3:30 PM,
Rest area 7.floor NHA

Continuing from last week, I will talk about Andrew Wiles' proof of the Taniyama-Shimura-Weil Conjecture, and why it implies Fermat's Last Theorem.

There will be served coffee, tea and biscuits from 14.00.

Time and place:
May 13, 2016 2:30 PM - 3:30 PM,
Rest area 7.floor NHA

In preparation for the Abel Prize week, I will talk about Fermat's Last Theorem and the Taniyama-Shimura-Weil Conjecture about the modularity of elliptic curves.

There will be served coffee, tea and biscuits from 14.00.

Time and place:
Feb. 25, 2016 2:30 PM - 3:30 PM,
Rest area 7.floor NHA

Abstract:

Let X=Spec(R) be a smooth affine variety and let Y be a closed subvariety corresponding to an ideal I in R. Finding a set of generators for I is in general a very hard problem, even in the case where X is an affine space over a field k. However, an easy application of Nakayama’s lemma shows that the number n of generators of I is at least the number m of generators of its conormal bundle and at most m+1. We will show how to actually determine when n=m using homotopical and cohomological methods, answering in particular a long standing conjecture of Murthy.

Coffee/Tea/Biscuit from 14.00

Time and place:
Dec. 11, 2015 2:30 PM - 3:30 PM,
Rest area 7.floor NHA

Time and place:
Sep. 11, 2015 2:30 PM - 3:30 PM,
Rest area 7 th. floor NHA

Abstract; Grassmannians and flag varieties play fundamental role in modern mathematics. They show up in many different situations and have been extensively studied from the point of view of algebraic geometry, topology,representation theory and combinatorics. In the first part of my talk I will recall the main properties of the Grassmannians and flag varieties. In particular, I will describe the connection with the representation theory of the general linear group. In the second part of the talk I will describe recent results on the Poincaré–Birkhoff–Witt degenerations. The main idea to be utilized is the connection between the representation spaces and the varieties we are interested in.

Coffee/Tea/Biscuits from 14.00

Time and place:
Apr. 24, 2015 2:30 PM - 3:30 PM,
Rest area 7 th. floor NHA

Abstract: If A×C ≃ B×C, is A ≃ B? We encounter this questions in many contexts, and the answer depends in often very subtle ways on the context, or in fancier language, on the category for which the question is posed. I will discuss some examples from algebra, for instance: does a polynomial ring uniquely determine its ring of coefficients, or in algebraic geometry, for instance: if X, Y, Z are algebraic varieties and X × Z ≃ Y ×Z, is X ≃ Y. Here, even when X,Y,Z are affine spaces, the answer (both yes and no occur) is known only in a few cases. In general, a lot of nice mathematics is involved both in proving positive results and in constructing counterexamples.

Coffee/Tea/Biscuits from 14.00

Time and place:
Apr. 10, 2015 2:30 PM - 3:30 PM,
NHA rest area

Modular symmetries have been central to many developments in mathematics since their discovery more than a century ago, including the proof of Fermat´s last theorem. In view of Nature´s love for order and symmetry, it is surprising that modular symmetry has not been found in the real world – until now.

Coffee/Tea/Biscuits from 14.00

Time and place:
Mar. 13, 2015 2:30 PM - 3:30 PM,
NHA rest area

*Abstract: **In this talk I briefly review the connection between these two areas **and describe basic structures and problems underlying both fields.*

Coffee/tea and cookies will be served from 14.00 to 14.30.

Time and place:
Dec. 12, 2014 2:00 PM - 3:00 PM,
Aud 4 VB

Abstract: Soliton equations are an important class of nonlinear partial differential equations, which contain physically relevant equations like the Korteweg-de Vries (KdV) equation, the sine-Gordon equation, and the Nonlinear Schrödinger equation. While these equations govern very different physical phenomena, they have striking common structural properties like the existence of particle-like solutions (solitons) interacting in elastic collisions. The struggle to find a mathematical explanation has led to substantial progress in mathematical physics. Today it is known that the theory of soliton equations is linked to several major branches of mathematics. Our talk will be an introduction to an operator theoretic approach to soliton equations, which may be traced back to work of Marchenkov and enables us to apply Banach geometry in the study of solution families. As a motivation, we will carefully explain this in the most accessible case of the KdV equation. Then we will discuss further developments of the method in the study of matrix equations and hierarchies. In the applications part, we will talk on the asymptotic description of multiple pole solutions, the construction of matrix solitons and countable nonlinear superposition. We will illustrate our results by Mathematica plots.

Coffee/tea and cookies will be served from 13.30 to 13.55 in the rest area, 7th floor, NHA.

Time and place:
Aug. 22, 2014 2:30 PM - 3:30 PM,
Pauseareal 7.etg. NHA

Abstract: I wish to give some insight into how a generalization of a question related to the limiting behaviour of sequences of large graphs allows for a fruitful interaction between ideas and methods from combinatorics, probability theory and functional analysis. Joint work with L. Lovász and B. Szegedy.

Time and place:
June 6, 2014 2:30 PM - 3:30 PM,
Rest area, 7th floor, NHA

Abstract: The idea of this talk is to introduce the concept of o-minimal theories and give a sense in how it can be useful in different areas of mathematics. O-minimality is a branch of model theory which is concerned with understanding "tame" analytic expansions of the real closed field. I will give definitions and state some of the main properties of o-minimality. I will also state and sketch applications to statistical learning theory and state some of the new applications to algebraic geometry and Diophantine number theory.

Coffee/tea and cookies from 14.00.

Time and place:
Feb. 10, 2014 2:30 PM - 3:30 PM,
Auditorium 2, V.B.

Abstract: In this talk, my goal is to give an introduction to some of the mathematics behind quasicrystals. Quasicrystals were discovered in 1982, when Dan Schechtmann observed a material which produced a diffraction pattern made of sharp peaks, but with a 10-fold rotational symmetry. This indicated that the material was highly ordered, but the atoms were nevertheless arranged in a non-periodic way.These quasicrystals can be defined by certain aperiodic tilings, amongst which the famous Penrose tiling. What makes aperiodic tilings so interesting--besides their aesthetic appeal--is that they can be studied using tools from many areas of mathematics: combinatorics, topology, dynamics, operator algebras... While the study of tilings borrows from various areas of mathematics, it doesn't go just one way: tiling techniques were used by Giordano, Matui, Putnam and Skau to prove a purely dynamical statement: any Z^d free minimal action on a Cantor set is orbit equivalent to an action of Z.

NB: Coffee/tea and cookies will served from 14.00-14.25 in the rest area of the 7th floor in NH Abel's House, as usual. Note that the colloquium talk will be held in Aud 2 VB from 14.30.

Time and place:
Nov. 19, 2013 2:30 PM - 3:30 PM,
Aud 2 VB

Judith Packer (University of Colorado at Boulder, USA) will give a Colloquium Talk:

Fractals, fractal wavelets, and measures on solenoids

Abstract: We discuss a construction, first due to D. Dutkay and P. Jorgensen, that can be used to define generalized wavelets on inflated fractal spaces arising from iterated function systems.

Self-similarity relations defining the fractal spaces also give rise to filter functions defined on the torus. These filter functions can be used to construct isometries, as well as probability measures on solenoids. Representations of the Baumslag-Solitar group can be obtained from the probability measures, and some properties of the representation are related to properties of the original wavelet and filter systems. Some results joint with L. Baggett, N. Larsen, K. Merrill, I. Raeburn, and A. Ramsay will be discussed.

NB: Coffee/tea and cookies will served from 14.00-14.25 in the rest area of the 7th floor in NH Abel's House, as usual. But note that the colloquium talk will be held in Aud 2 VB from 14.30.

Time and place:
June 19, 2013 2:30 PM - 3:30 PM,
Rest area 7. floor NHA

Abstract: Rudin's classic treatise "Function Theory in Polydiscs" from 1969 studies complex analysis on polydiscs starting from the following question: How much of our extremely detailed knowledge about holomorphic functions in the unit disc can be carried over to an analogous situation in several variables, namely to polydiscs? A different perspective comes from the work of Bohr and Bohnenblust--Hille several decades earlier; here the main issue is function theory in the infinite-dimensional polydisc, which to a large extent is concerned with the asymptotics of function theory in finite-dimensional polydiscs. I will discuss some examples, old and new, of what these different viewpoints have led to, as well as connections to other areas.

There will be served coffee, tea and biscuits from 14.00.

Time and place:
Mar. 22, 2013 2:30 PM - 3:30 PM,
Pauseareal 7.etg NHA

Abstract: In this talk we will discuss some of the foundations of computational mathematics. In particular, I will ask the rather fundamental questions: "Can everything be computed?" and: "In what way?" and discuss possible ways to answer them. This is done by linking some new developments in computational mathematics (in particular the Solvability Complexity Index and towers of algorithms) to some of the fundamental works of Godel, McMullen and Smale

Time and place:
Apr. 27, 2012 2:30 PM - 3:30 PM,
Pauseareal 7.etg NHA

In 1975 this year's Abel Prize recipient, the Hungarian mathematician Endre Szemerédi, proved a long-standing conjecture of Erdøs: if A is a subset of the natural numbers of positive upper density, then A contains arbitrarily long arithmetic progressions. His proof is purely of combinatorial nature and extremely complicated--only a handful people have read and understood it. In 1977 Furstenberg gave a new proof using ergodic theory. Specifically, he showed that any measure-preserving system has a multiple recurrence property, which is a vast generalization of a classical result of Poincaré. What is amazing is that Szemerédi's theorem and Furstenberg's theorem actually are equivalent! We will indicate how the Szemeredi theorem -- and Furstenberg's proof of it -- plays a key role in the proof of the now famous Green/Tao result from 2004: within the prime numbers there exist arbitrarily long arithmetic progressions.