Mon, 19 Feb 2024

16:30 - 17:30
L5

Sharp stability for Sobolev and log-Sobolev inequalities, with optimal dimensional dependence

Rupert Frank
(LMU Munich)
Abstract

The sharp constant in the Sobolev inequality and the set of optimizers are known. It is also known that functions whose Sobolev quotient is almost minimial are close to minimizers. We are interested in a quantitative version of the last statement and present a bound that not only measures this closeness in the optimal topology and with the optimal exponent, but also has explicit constants. These constants have the optimal behavior in the limit of large dimensions, which allows us to deduce an optimal quantitative stability estimate for the Gaussian log-Sobolev inequality with an explicit dimension-free constant. Our proof relies on several ingredients:

• a discrete flow based on competing symmetries;

• a continuous rearrangement flow;

• refined estimates in the neighborhood of the optimal Aubin-Talenti functions.

The talk is based on joint work with Dolbeault, Esteban, Figalli and Loss. 


 
Wed, 30 Nov 2022
16:00
L4

Handlebody groups and disk graphs

Panagiotis Papadopoulos
(LMU Munich)
Abstract

The handlebody group is defined as the mapping class group of a three-dimensional handlebody. We will survey some geometric and algebraic properties of the handlebody groups and compare them to those of two of the most studied (classes of) groups in geometric group theory, namely mapping class groups of surfaces, and ${\rm Out}(F_n)$. We will also introduce the disk graph, the handlebody-analogon of the curve graph of a surface, and discuss some of its properties.

Thu, 18 May 2017

16:00 - 17:30
L4

Financial Asset Price Bubbles under Model Uncertainty

Francesca Biagini
(LMU Munich)
Abstract

We  study  the  concept  of   financial  bubble  under model uncertainty.
We suppose the agent to be endowed with a family Q of local martingale measures for  the  underlying  discounted  asset  price. The priors are allowed to be mutually singular to each other.
One fundamental issue is the definition of a well-posed concept of robust fundamental value of a given  financial asset.
Since in this setting we have no linear pricing system, we choose to describe robust fundamental values through superreplication prices.
To this purpose, we investigate a dynamic version of robust superreplication, which we use
to  introduce  the  notions  of  bubble  and  robust  fundamental  value  in  a  consistent way with the existing literature in the classical case of one prior.

This talk is based on the works [1] and [2].

[1] Biagini, F. , Föllmer, H. and Nedelcu, S. Shifting martingale measures
and the slow birth of a bubble as a submartingale, Finance and
Stochastics: Volume 18, Issue 2, Page 297-326, 2014.


[2] Biagini, F., Mancin, J.,
Financial Asset Price Bubbles under Model 
Uncertainty, Preprint, 2016.

Wed, 21 May 2014

15:00 - 16:00
L5

Pointwise estimates for degenerate elliptic systems

Dr Dominic Breit
(LMU Munich)
Abstract

We consider degenerate elliptic systems like the p-Laplacian  system with p>1 and zero boundary data. The r.h.s. is given in  divergence from div F. We prove a pointwise estimate (in terms of the  sharp maximal function) bounding the gradient of the solution via the  function F. This recovers several known results about local regularity  estimates in L^q, BMO and C^a. Our pointwise inequality extends also  to boundary points. So these  regularity estimates hold globally as  well. The global estimates in BMO and C^a are new.

Mon, 26 Nov 2012

12:00 - 13:00
L3

Scanning for stabilizing bundles in heterotic vacua

James Gray
(LMU Munich)
Abstract
I will describe methods for searching for bundles which are only holomorphic for isolated complex structures of a base Calabi-Yau threefold. These can be used, in the hidden sector of heterotic compactifications, to stabilize the associated moduli fields. Various bundle constructions will be covered, and the possibility and consequences of resolving the potentially singular threefolds which result will be discussed. If time permits, I will also briefly mention a large set of Calabi-Yau fourfolds which is currently being classified.
Mon, 17 Oct 2011

12:00 - 13:00
L3

A ten-dimensional action for non-geometric fluxes

David Andriot
(LMU Munich)
Abstract

Four-dimensional (4d) supergravities with non-geometric terms in their potential are very promising models for phenomenology. Indeed, these terms, generated by so-called non-geometric fluxes, generically help to obtain de Sitter vacua, or to stabilise moduli. Unfortunately, deriving these theories from a compactified ten-dimensional (10d) supergravity has not been achieved so far. One reason is that non-geometric fluxes do not seem to match any 10d field, and another reason is the appearance of global issues in 10d non-geometric configurations.

After reviewing some background material, we present in this talk a solution to the two previous issues. Thanks to a field redefinition, we make the non-geometric Q-flux appear in a 10d action, which only differs from the NSNS action by a total derivative. In addition, this new action is globally well-defined, at least in some examples, and one can then perform the dimensional reduction to recover the 4d non-geometric potential. We also mention an application to the heterotic string.

Based on 1106.4015.

Mon, 06 Jun 2011

12:00 - 13:00
L3

String compactifications on toric varieties

Magdalena Larfors
(LMU Munich)
Abstract
In the absence of background fluxes and sources, compactifying string theories on Calabi-Yau three-folds leads to supersymmetric solutions. Turning on fluxes, e.g. to lift the moduli of the compactification, generically forces the three-fold to break the Calabi-Yau conditions, and instead fulfill the weaker geometrical condition of having a reduced structure group. In this talk I will demonstrate that three-dimensional smooth, compact, toric varieties can have reduced structure group, and thus be suitable for flux compactifications of string theory. Since the class of three-dimensional SCTV is large, this is promising for the construction of new, phenomenologically interesting string theory vacua.
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