Lincoln Wallen is the Former CTO, Dreamworks Animation. All are welcome

# Past Special Lecture

Today, everyone knows everything: with only a quick trip through WebMD or Wikipedia, average citizens believe themselves to be on an equal intellectual footing with doctors and diplomats. All voices, even the most ridiculous, demand to be taken with equal seriousness, and any claim to the contrary is dismissed as undemocratic elitism. Tom Nichols argues that in this climate, democratic institutions themselves are in danger of falling either to populism or to technocracy- or in the worst case, a combination of both.

Tom Nichols is Professor of National Security Affairs at the US Naval War College, an adjunct professor at the Harvard Extension School, and a former aide in the U.S. Senate. His latest book is The Death of Expertise: The Campaign Against Established Knowledge and Why it Matters. This lecture is based on that book.

All welcome. No need to book.

Timetable:

1.00pm: Introductory Remarks by Camilla Serck-Hanssen, the Vice President of the Norwegian Academy of Science and Letters

1.10pm - 2.10pm: Andrew Wiles

2.10pm - 2.30pm: Break

2.30pm - 3.30pm: Irene Fonseca

3.30pm - 4.00pm: Tea and Coffee

4.00pm - 5.00pm: John Rognes

Abstracts:

Andrew Wiles: Points on elliptic curves, problems and progress

This will be a survey of the problems concerned with counting points on elliptic curves.

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Irene Fonseca: Mathematical Analysis of Novel Advanced Materials

Quantum dots are man-made nanocrystals of semiconducting materials. Their formation and assembly patterns play a central role in nanotechnology, and in particular in the optoelectronic properties of semiconductors. Changing the dots' size and shape gives rise to many applications that permeate our daily lives, such as the new Samsung QLED TV monitor that uses quantum dots to turn "light into perfect color"!

Quantum dots are obtained via the deposition of a crystalline overlayer (epitaxial film) on a crystalline substrate. When the thickness of the film reaches a critical value, the profile of the film becomes corrugated and islands (quantum dots) form. As the creation of quantum dots evolves with time, materials defects appear. Their modeling is of great interest in materials science since material properties, including rigidity and conductivity, can be strongly influenced by the presence of defects such as dislocations.

In this talk we will use methods from the calculus of variations and partial differential equations to model and mathematically analyze the onset of quantum dots, the regularity and evolution of their shapes, and the nucleation and motion of dislocations.

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John Rognes: Symmetries of Manifolds

To describe the possible rotations of a ball of ice, three real numbers suffice. If the ice melts, infinitely many numbers are needed to describe the possible motions of the resulting ball of water. We discuss the shape of the resulting spaces of continuous, piecewise-linear or differentiable symmetries of spheres, balls and higher-dimensional manifolds. In the high-dimensional cases the answer turns out to involve surgery theory and algebraic K-theory.

In this year’s Simonyi Lecture, Geoffrey West discusses the universal laws that govern everything from the growth of plants and animals to cities and corporations. These laws help us to answer big, urgent questions about global sustainability, population explosion, urbanization, ageing, cancer, human lifespans and the increasing pace of life.

Why can we live for 120 years but not for a thousand? Why do mice live for just two or three years and elephants for up to 75? Why do companies behave like mice, and are they all destined to die? Do cities, companies and human beings have natural, pre-determined lifespans?

Geoffrey West is a theoretical physicist whose primary interests have been in fundamental questions in physics and biology. West is a Senior Fellow at Los Alamos National Laboratory and a distinguished professor at the Sante Fe Institute, where he served as the president from 2005-2009. In 2006 he was named to Time’s list of The 100 Most Influential People in the World.

This lecture will take place at the Oxford Playhouse, Beaumont Street. Book here

Abstract: If A is a finite dimensional algebra, and D(A) the unbounded

derived category of the full module category Mod-A, then it is

straightforward to see that D(A) is generated (as a "localizing

subcategory") by the indecomposable projectives, and by the simple

modules. It is not so obvious whether it is generated by the

indecomposable injectives. In 2001, Keller gave a talk in which he

remarked that"injectives generate" would imply several of the well-known

homological conjectures, such as the Nunke condition and hence the

generalized Nakayama

conjecture, and asked if there was any relation to the finitistic

dimension conjecture. I'll show that an algebra that satisfies "injectives

generate" also satisfies the finitistic dimension conjecture and discuss

some examples. I'll present things in a fairly concrete way, so most of

the talk won't assume much knowledge of derived categories.

Abstract: In this talk I will discuss the interplay between the local and

the global invariants in modular representation theory with a focus on the

first Hochschild cohomology $\mathrm{HH}^1(B)$ of a block algebra $B$. In

particular, I will show the compatibility between $r$-integrable

derivations

and stable equivalences of Morita type. I will also show that if

$\mathrm{HH}^1(B)$ is a simple Lie algebra such that $B$ has a unique

isomorphism class of simple modules, then $B$ is nilpotent with an

elementary abelian defect group $P$ of order at least 3. The second part

is joint work with M. Linckelmann.

Abstract: I will describe how the ADE preprojective algebras appear in

certain Conformal Field Theories, namely SU(2) WZW models, and explain

the generalisation to the SU(3) case, where 'almost CY3' algebras appear.

Abstract: In this talk, we will introduce new affine algebraic varieties

for algebras given by quiver and relations. Each variety contains a

distinguished element in the form of a monomial algebra. The properties

and characteristics of this monomial algebra govern those of all other

algebras in the variety. We will show how amongst other things this gives

rise to a new way to determine whether an algebra is quasi-hereditary.

This is a report on joint work both with Ed Green and with Ed Green and

Lutz Hille.

Abstract: This is joint work with Ragnar-Olaf Buchweitz and Colin Ingalls.

The classical McKay correspondence relates the geometry of so-called

Kleinian surface singularities with the representation theory of finite

subgroups of SL(2,C). M. Auslander observed an algebraic version of this

correspondence: let G be a finite subgroup of SL(2,K) for a field K whose

characteristic does not divide the order of G. The group acts linearly on

the polynomial ring S=K[x,y] and then the so-called skew group algebra

A=G*S can be seen as an incarnation of the correspondence. In particular

A is isomorphic to the endomorphism ring of S over the corresponding

Kleinian surface singularity.

Our goal is to establish an analogous result when G in GL(n,K) is a finite

subgroup generated by reflections, assuming that the characteristic

of K does not divide the order of the group. Therefore we will consider a

quotient of the skew group ring A=S*G, where S is the polynomial ring in n

variables. We show that our construction yelds a generalization of

Auslander's result, and moreover, a noncommutative resolution of the

discriminant of the reflection group G.

Abstract: Joint work with Carlson, Grodal, Nakano. In this talk we will

present some recent results on an 'important' class of modular

representations for an 'important' class of finite groups. For the

convenience of the audience, we'll briefly review the notion of an

endotrivial module and present the main results pertaining endotrivial

modules and finite reductive groups which we use in our ongoing work.