# Talks

Talks displayed in this page are ordered by alphabetical order of the speakers' surnames. The schedule can be consulted in the schedule page.
The talks will take place at the Einstein-Saal of the Berlin-Brandenburg Academy of Sciences and Humanities. More information about the location can be found in the venue page.
All talks will be probably recorded in video, but the video will be released publicly only upon permission of the speaker.

TBA

## Invited Talks

Talks are ordered alphabetically with respect the speakers. Abstracts will be added as they are being received.

### The square root of the dimension

#### Carlos Beltrán (Universidad de Cantabria)

...where a gorgeous result by Felipe Cucker is revisited, the solution to a famous problem is shown, and a theorem that is not a theorem is proved to be useful, but not necessarily in that order.

### Nonlinear Korn inequalities on a surface

#### Philippe Ciarlet (City University of Hong Kong)

It is well known that a surface can be recovered from its two fundamental forms if they satisfy the Gauss and Codazzi-Mainardi compatibility equations on a simply-connected domain, in which case the surface is uniquely determined up to isometric equivalence. It is less known that in this case the surface becomes a continuous function of its fundamental forms, again up to isometric equivalence, for various topologies, such as the Fréchet topology of continuously differentiable functions, or those corresponding to various Sobolev norms.

In this talk, we will review such continuity results obtained during the past fifteen years, with special emphasis on those that can be derived by means of nonlinear Korn inequalities on a surface.We will also mention potential applications of such results, such as the intrinsic approach to nonlinear shell theory, where the unknowns are the fundamental forms of the deformed middle surface of a shell.

### Combinatorial Nullstellensatz, Fewnomials, $$\tau$$-Conjecture in Tropical Algebra

#### Dima Grigoriev (CNRS)

Tropical analogs of the combinatorial Nullstellensatz, universal testing set for fewnomials and $$\tau$$-conjecture are provided.

### The incredible shrinking algebraic computation model

#### Pascal Koiran (Ecole Normale Supérieure de Lyon)

In the 1957 movie "the incredible shrinking man", a businessman is exposed to radioactive dust and begins to shrink while researchers try and fail to stop that process. In this talk we will see what happens if, instead of a human being, we shrink the computation model that the researchers study.

### Stochastic Gradient Descent and Perceptron Boundedness

#### Raphael Hauser (University of Oxford)

The development of stochastic gradient descent type algorithms (SGD) have been a major factor in allowing optimisation methods to be successfully applied to ever larger data analytics and machine learning problems. In applications it is often observed that if SGD is stopped early rather than being left to complete its calculations to a high accuracy termination criterion, the resulting solutions are of greater practical relevance. In this talk we will shed some light on this phenomenon, by relating the problem of minimising objective functions in the form of a sum of simple functions to the maximum feasible subsystem problem and perceptron boundedness, the latter being characterised by a condition number. Under this interpretation, early stopping of SGD yields solutions to a robust version of the underlying optimisation problem.

### Logic and Computation: Felipe's Work on Descriptive Complexity

#### Klaus Meer (BTU Cottbus)

There is a long and fruitful interplay between the fields of logic and computation. One of its examples is the field of descriptive complexity. Among the many fields in which Felipe Cucker worked (and works) descriptive complexity has been one. In this talk we want to review some of the results in this area with particular emphasis on joint work done many years ago with Felipe Cucker.

### The Hoffman constant of a system of linear inequalities

#### Javier Peña (Carnegie Mellon)

A classical result of Alan Hoffman from 1952 shows that if a point  almost satisfies a system of linear inequalities, then it is near an  actual solution to the system of linear inequalities.  We provide a  novel characterization of the sharpest Hoffman constant associated to  this "almost implies near" relationship.  Our characterization extends  to the more general case when some inequalities are easy to satisfy as  in the case of box constraints.  Our characterization also yields a  procedure to compute the Hoffman constant – a notoriously difficult and  largely unexplored computational challenge.

### Models for the heart beat

#### Steve Smale (Berkeley)

Certain cells in the heart called myocytes put into a petri dish will oscillate individually until they become close together when they start to beat in unison.  The mathematics goes  back more than 350 years  with Huygens and is still trying to give a good picture.  I have been working with Indika Rajapakse and Charles Pugh on these things and we have been led to a fascinating complex of problems and insights into the  dynamics of the heart beat.

### The zero set of the independence polynomial of a graph

#### Martín Sombra (ICREA & Universitat de Barcelona)

In statistical mechanics, the independence polynomial of a graph arises as the partition function of the hard-core lattice gas model. The distribution of the zeros of these polynomials at the thermodynamic limit is expected to be relevant for the study of the model and, in particular, for the determination of its phase transitions. In this talk, I will review the known results on the location of these zeros, with emphasis on the case of rooted regular trees of fixed degree and varying depth. Our main result states that for these graphs, the zero sets of their independence polynomials converge as the depth increases towards the bifurcation measure of a certain family of dynamical systems on the Riemann sphere.

This is ongoing work with Juan Rivera-Letelier (Rochester)

### Average minus Weak Complexity equals Adaptive algorithms

#### Josué Tonelli-Cueto (Technische Universität Berlin)

In 1999 Felipe Cucker introduced the real global condition number, fondly known as $$\kappa$$ (kappa), in his seminal paper "Approximate zeros and condition numbers". This condition number and its variations are widely believed to capture the numerical complexity of problems in real algebraic geometry. In this talk, we show that this is not the case and that a new condition-based approach might open the door to finite expectation algorithms in numerical real algebraic geometry.