Fachbereich Mathematik und Statistik Universität Konstanz

# Konstanz Women in Mathematics: Paths in Studies and Career

The information and discussion platform "Konstanz Women in Mathematics: paths in studies and in career" (KWIM) intends to be:
• a lecture series aimed to present mathematical results/biographies of female mathematicians and/or their experience in academia.
• a meeting point for female mathematicians which intends to promote them in their paths in studies and career.
• a counseling by women for women.
This project is supported by the Equal Opportunity Council at the University of Konstanz from 01.01.2016 to 31.12.2018 under the project number FP689/14 and coordinated by Maria Infusino as academic assistant of Salma Kuhlmann. On this webpage you can find all the activities within this project.

If you are interested in knowing more about the KWIM project and its activities, please download the KWIM presentation given by Maria Infusino on October 26th 2016. More details about KWIM past activities can be found here .

Guidelines: If you would like to suggest guests or to give yourself a presentation in this lecture series, please contact at least 15 days in advance: Maria Infusino (maria.infusino@uni-konstanz.de) .

# NEWS!

• KWIM-Festtage, University of Konstanz, December 6th-7th, 2018

• # KWIM Lectures Series 2018/2019

Where available, you can download the pdf-file of a talk by clicking on its title in the list below.
• Elisa Iacomini (La Sapienza University, Italy): A new multi-scale model for traffic flow
Tuesday November 20th 2018, 17:00 - 18:15, Room F426
Abstract.
Nowadays, the exponentially increasing number of cars and vehicles along the roads leads the researchers to find an accurate model to reproduce the traffic conditions and make reliable forecasts. There are two different approaches to model traffic flow phenomena, which differ from each other in the scale of representation. Microscopic models look at the motion of each single vehicle, predicting the evolution of its position and speed by means of a system of ordinary second-order differential equations. On the other hand, macroscopic models provide a large-scale aggregate point of view by means of partial differential equations. In this talk I will present a new kind of model for traffic flow which couples a first-order macroscopic approach with a second-order microscopic approach, avoiding any interface or boundary conditions between them. The numerical scheme associated to the model is conservative and it is able to reproduce typical traffic phenomena like stop & go waves shown in the numerical tests. This is a joint work with Emiliano Cristiani.

# KWIM Lectures Series 2017/2018

Where available, you can download the pdf-file of a talk by clicking on its title in the list below.
• Carolin Antos-Kuby (Universität Konstanz, Germany): True, false, independent: How the Continuum Hypothesis can be solved (or not).
Tuesday December 12th 2017, 17:00 - 18:15, Room F426
Abstract.
What is the size of the set of real numbers? The search for the answer to this question led the way to the development of one of the most productive and powerful techniques in modern set theory - the forcing technique. It was developed to find an answer to the question of the truth of the Continuum Hypothesis (CH), a statement that says that there is no infinite cardinality between that of the natural and the real numbers. The answer to this question is, in a nutshell: Some people think it is true, some think it is false, all know that it is independent and nowadays one could argue that it is all three at once.
To illustrate this answer I will focus on different models of set theory and how to construct them in a way that renders CH true or false. We will look at the constructible universe L that was build by Kurt Gödel and give an introduction to the forcing method. Forcing was developed to decide CH, but it is actually a general technique that allows one to build models suited to a vast varieties of set theoretic tasks. We will give an overview of the technical set-up of forcing and detail on how it can be used to build a model where CH is false. We conclude by considering the behavior of CH over a multitude of set-theoretic models created by forcing that decide CH in very different ways.

• Julia Lieb (Universität Würzburg, Germany): MDP Faltungscodes
Tuesday February 13th 2018, 17:00 - 18:15, Room F426
Abstract.
Das Prinzip fehlerkorrigierender Codes ist es, an eine Nachricht (Folge von Elementen eines endlichen Körpers) vor dem Senden Redundanz anzufügen, um die ursprüngliche Nachricht wieder rekonstruieren zu können, wenn beim Senden Fehler oder Informationsverlust auftreten. Hierbei ist der Minimalabstand zwischen Codewörtern entscheidend für die Anzahl der Fehler, die korrigiert werden können. Das Thema dieses Vortrages sind MDP Faltungscodes. Diese besitzen die Eigenschaft, dass der sog. Spaltenabstand für so lange wie möglich so schnell wie möglich wächst. Der Vortrag beginnt mit einer kurzen Einführung zur Kodierungstheorie und zu MDP Faltungscodes. Darüber hinaus werden reversible und vollständige MDP Faltungscodes betrachtet, die vorteilhafte Zusatzeigenschaften besitzen. Es wird die Existenz dieser Codes für alle Codeparameter gezeigt. Danach werden allgemeine Konstruktionstechniken vorgestellt, die voraussetzen, dass die Größe des zugrundeliegenden endlichen Körpers hinreichend groß ist. Schließlich wird für spezielle Codeparameter die Frage untersucht, welche Größe des Körpers notwendig ist, damit es möglich ist, einen MDP Faltungscode zu konstruieren.

• Anna-Lena Horlemann-Trautmann (University of St. Gallen, Switzerland): An Introduction to (Network) Coding Theory
Tuesday April 24th 2018, 17:00 - 18:15, Room F426
Abstract.
Coding theory deals with the question how to make digital data more resilient against noise (naturally occurring errors) during communication. We encode the data before sending it by adding some redundancy which can be used for error detection and correction at the receiver. One of the main research goals is to find ways to add redundancy in a smart way, such that the number of correctable errors is as large as possible, while keeping the redundancy as low as possible. Many classical results in this regard use algebraic tools like polynomials or vector spaces over finite fields. In contrast to classical coding theory, where we study a communication channel from one sender to one receiver, the network coding model has one sender and many receivers, all of which want to receive the same message from the sender. In this model, the noise behaves differently and it turns out that one can improve the tradeoff of redundancy and error correction by designing new codes for this setup, instead of using the known classical codes. In this talk we will give an introduction to the topic and an overview of important results for both classical coding theory and network coding theory.

• Giulia Fabrini (Universität Konstanz, Germany): Numerical approximation for optimal control problem via MPC and HJB
Tuesday May 15th 2018, 17:00 - 18:15, Room F426
Abstract.
The theory of control analyses the properties of controlled systems, i.e. dynamical systems on which we can act through a function called control. The aim is to bring the system from an initial state to a certain final state satisfying some criteria. There are two different types of control: open-loop controls, which depend on the time variable and feedback controls, which depend on the state variable. The second ones are more appealing since they are robust to external perturbations. However, the synthesis of feedback controls requires the solution of a nonlinear Hamilton-Jacobi-Bellman equation (HJB). Due to the complexity of finding an analytical solution to this equation, several approximations schemes have been proposed. The major bottleneck of these numerical schemes is that they suffer from the so called  "curse of dimensionality”, since the dimension of the discretised equation increases as the dimension of the state space does. An alternative way to find control in feedback form is a method known as Model Predictive Control (MPC).  In this talk we give an introduction to the HJB and MPC approaches and also propose a coupling of them.  Finally, we present some numerical tests to show the efficiency of the proposed algorithm.

• Sabine Jansen (LMU München, Germany): Phase transitions for interacting particles in $\mathbb R^d$
Tuesday May 29th 2018, 17:00 - 18:15, Room F426
Abstract.
Probability theory helps to understand systems made of many individual agents with random behavior. One question of interest is: How is it possible that collective orderly behavior emerges out of individual randomness? Does collective behavior depend in a smooth fashion on underlying system parameters? In statistical physics, the individual "agents" are particles (atoms, molecules...) and the questions are intimately tied to the theory of phase transitions - e.g., from ice to liquid water to vapor. A satisfactory theory for particles in $\mathbb R^d$ is still elusive. The talk will introduce some notions on statistical physics and present some partial results.

• Federica Gregorio (Università degli Studi di Salerno, Italy): Elliptic operators with unbounded coefficients
Friday June 8th 2018, 11:45 - 13:15, Room G530
Abstract.
Recently the interest in operators with unbounded coefficients has grown considerably due to their numerous applications in many fields of science, such as quantum mechanics, fluid dynamics, e.g., in the study of Navier-Stokes equations with a rotating obstacle. Moreover the main applications are in stochastic analysis and mathematical finance, where stochastic models lead to equations with unbounded coefficients, e.g., the well known Black-Scholes equation and some structure models of interest rate derivatives. This class of operator is a generalisation of the operators with bounded coefficients and historically, in the mathematical literature, the subject is studied using several approaches, with ideas and methods from partial differential equations, Dirichlet forms, stochastic processes, stochastic differential equations. After a general framework of the topic we focus on the elliptic operator $$A=(1+|x|^{\alpha})\Delta+b|x|^{\alpha-1}\frac{x}{|x|}\cdot \nabla-c|x|^{\beta}.$$ We prove that the realization $A_p$ in $L^p(\mathbb{R}^N)$,\,$1< p <\infty$, of $A$ with domain $D(A_p) =\{ u \in W^{2,p}(\mathbb{R}^N)\, |\, Au \in L^p(\mathbb{R}^N)\}$ generates a strongly continuous analytic semigroup $T(\cdot)$ provided that $\alpha >2,\,\beta >\alpha -2$ and any constants $b\in \mathbb{R}$ and $c>0$. Moreover we show that $T(\cdot)$ is consistent, immediately compact and ultracontractive.

• Karin Baur (Universität Graz, Austria): Interactions between Algebra and Geometry
Tuesday June 12th 2018, 17:00 - 18:15, Room F426
Abstract.
Algebra, Geometry and Combinatorics are closely linked. Starting from classical theorems by Pythagoras and Ptolemy we will discuss the combinatorics of triangulations of surfaces. This yields a beautiful approach to cluster algebras, a young and thriving research area with links to various fields in Mathematics. Of particular interest are approaches to Grassmannian Cluster algebras with their impact on representation theory.

• Nalini Anantharaman (Université de Strasbourg, France): Quantum ergodicity and delocalization of Schrödinger eigenfunctions
Tuesday June 19th 2018, 17:00 - 18:15, Room F426
Abstract.
The question of ''quantum ergodicity'' is to understand how the ergodic properties of a classical dynamical system are translated into spectral properties of the associated quantum dynamics. This question can be traced back to a paper by Einstein written in 1917. It takes its full meaning after the introduction of the Schrödinger equation in 1926, and even more after the numerical simulations of the 80s that seem to indicate that, for chaotic'' classical dynamics, the spectrum of the associated Schrödinger operator resembles that of a class of large random matrices. Proving this is still fully open. However, we start to understand quite well how the chaotic properties of classical dynamics lead to delocalization properties of the wave functions. We will review the results on the subject and some examples.

• KWIM presents: Studying abroad with ALGANT on Tuesday June 26th 2018, 17:00, Room F426
• 17:00 - 17:45: Lecture on ''Configurations of lines on del Pezzo surfaces '' by Rosa Winter (University of Leiden, Netherlands):
Abstract.
Del Pezzo surfaces are surfaces that can be obtained from the plane by a construction called blow-up. They can be classified by their degree, and we know exactly how many lines are contained in these surfaces over an algebraically closed field. Famous examples are smooth cubic surfaces in the space $\mathbb{P}^3$, which are del Pezzo surfaces of degree three. These contain 27 lines, of which at most three can go through the same point. Similarly, a del Pezzo surface of degree two contains 56 lines, of which at most four can go through the same point. In both of these cases, this maximum is given by the incidence graph of the lines in the surface. In this talk I will show how del Pezzo surfaces can be constructed and how we can and the lines on them. Then I will look at del Pezzo surfaces of degree one, which contain 240 lines. I will explain how we studied the large incidence graph on these lines, and how we used this and some classical geometry to show that in most characteristics the number of lines through one point is less than the bound given by the incidence graph. This is joint work with Ronald van Luijk.
• 17:45 - 18:15: Presentation of the ALGANT Master programme by Michele Serra (University of Konstanz, Germany) and Rosa Winter (University of Leiden, Netherlands)
• 18:15 - 18:30: Presentation about other opportunities to study abroad by Constanze Mittag (International Office, University of Konstanz, Germany)
• 18:30 -> Aperitif with refreshments

• Constanza Rojas-Molina (Heinrich-Heine-Universität Düsseldorf, Germany): Random Schrödinger Operators arising in the study of aperiodic media.
Tuesday July 3rd 2018, 17:00 - 18:15, Room F426
Abstract.
In this talk we review some results on random Schrödinger operators, a standard framework for the study of disordered quantum systems and the absence of wave propagation in random media, a phenomenon known as Anderson localization. Our goal is to apply these results to the study of spectral and dynamical properties of Delone operators, which serve to model aperiodic structures (quasi-crystals). As a consequence, we will show that aperiodic media, although usually associated to singular continuous spectrum and anomalous transport, does exhibit often Anderson localization and, in particular, pure point spectrum.

# KWIM Lectures Series 2016/2017

Where available, you can download the pdf-file of a talk by clicking on its title in the list below.
• Mickaël Matusinski (Universiteé Bordeaux, France): Sofia Kovalevskaya : mathematician, writer, revolutionnary.
Tuesday January 17th 2016, 17:00 - 18:15, Room D432
Abstract.
Sofia Kovalevskaya is a prominent historical personality. She used to be a full leading mathematician of her time, at an international level, thanks to her rich and varied works that are taught everywhere and continue to inspire us. She was also - and not less - a militant socialist and feminist, and a committed novelist, emblematic figure of the Russian - and even European - intelligentsia rebeling during an era of historical upheavals. We will address these different aspects of her life.

• Diana Conache (TU München, Germany): Equilibrium states of interacting particle systems.
Tuesday February 9th 2016, 17:00 - 18:15, Room G300
Abstract.
Interacting particle systems are an increasingly popular field of study, due to applications not only in physics, but also in biology, ecology, economy, sociology, etc. Their mathematical modelling involves a beautiful mixture of techniques from analysis and probability alike. In this talk, I will focus on describing their behaviour in equilibrium and answer questions like: Can the system reach equilibrium? Is the equilibrium state unique? We will review some of the most important results in the literature and present some recent ones as well, focusing on the case of systems in the continuum.

• Jihad A. Titi (Universität Konstanz, Germany): Matrix methods for an efficient computation of the tensorial Bernstein coefficients.
Tuesday May 31st 2016, 17:00 - 18:15, Room F426
Abstract.
Solving optimization problems is of paramount importance in many real-life and scientific problems; polynomial global optimization problems form a significant part of them. Considered problems are unconstrained and constrained optimization problems over boxes. One approach for their solution is based on the expansion of a polynomial into Bernstein polynomials of the objective function and the constraints polynomials, the so-called Bernstein form. The coefficients (Bernstein coefficients) can be rearranged in a multi-dimensional array, the so-called Bernstein patch. From these coefficients we get bounds for the range of the objective function and the constraints over a box. We can improve the enclosure for the range of the polynomial by elevating the degree of the Bernstein expansion or by subdivisions of the region. In this talk, multivariate polynomials in the Bernstein basis over a box (tensorial Bernstein form) will be considered. Two new matrix methods for the computation of the polynomial coefficients with respect to the Bernstein basis will be presented and compared with existing methods. Also, matrix methods for the calculation of the Bernstein coefficients over subboxes generated by subdivision of the original box will be introduced.

• Lyudmila Grigoryeva (Universität Konstanz, Germany): Time-delay differential equations in machine learning.
Tuesday June 21st 2016, 17:00 - 18:15, Room F426
Abstract.
Reservoir computing is a recently introduced brain-inspired machine learning paradigm. We focus on a specific type of reservoir computers that is based on the use of time-delay differential equations. We call them time-delay reservoirs (TDRs). TDRs have been physically implemented using optical and electronic systems showing unprecedented data processing rates. We study the performance of TDRs in different working regimes and establish their functional link with the reservoir parameters. We focus on the stability analysis of the underlying time-delay differential equation and propose an approximating model that allows us to explore various properties of the device and to choose the optimal reservoir architecture, thus replacing tedious and time consuming parameter scannings used so far in the literature. In the proposed framework we tackle standard machine learning tasks of forecasting and reconstruction of stochastic time series. The discussed novel machine learning technique shows excellent potential in high-dimensional classification problems.

• KWIM Double Lecture: Tuesday July 5th 2016, 16:00 - 18:30, Room R512
• 16:00-17:00 Raman Parimala (Emory University, Atlanta, USA): Hasse principle over function fields
Abstract.
The classical theorem of Hasse and Minkowski asserts that a quadratic form over the field of rational numbers represents zero nontrivially provided that it represents zero nontrivially over completions at all its places. Analogous questions for function fields have interesting consequences. We shall discuss the analogy between the field of rational numbers and function fields of p-adic curves in the context of Hasse principles for quadratic forms and more general structures.
• 17:15-18:15 Charu Goel (Indian Institute of Science Education and Research, Mohali, India): Cones in and around the sum of squares cone
Abstract.
In this talk we will first introduce cones of sums of squares of k-term forms, which are more restrictive than the sums of squares cone. We then present some relevant worked out examples to show how these cones look like and relate to each other. Finally, we will describe cones of forms, which correspond to existence of a Gram matrix that is non-negative on varieties containing the Veronese variety, and explain how this gives us a nice filtration of intermediate cones between the sums of squares cone and the cone of positive semidefinite forms.

• Frauke Liers (Universität Erlangen-Nürnberg, Germany): Robust solution approaches for optimization under uncertainty: applications to air traffic management problems
Tuesday November 15th 2016, 17:00 - 18:15, Room F426
Abstract.
Real applications often face uncertainty in the input parameters. Robust optimization takes these uncertainties into account already in the mathematical model. The task is to determine solutions that are feasible for all considered realizations of the uncertain parameters, and among them one with best guaranteed solution value. In this talk, we focus on efficient planning of runway utilization under uncertainty as this is one of the main challenges in air-traffic management. We present optimization approaches for runway scheduling as well as for the pre-tactical planning phase. Mathematically, this leads to NP-hard optimization problems in which b-matchings with side constraints need to be determined. We present structural insights as well as effective exact solution algorithms. In reality, uncertainty and inaccuracy almost always lead to deviations from the actual schedule. We present robust optimization approaches together with computational results that show their effectiveness. These approaches are integrated and validated within simulation procedures. It is shown that the models that the robust models yield considerably more stable plans than the approaches that ignore uncertainties, at the price of limited increase in delay only.

• Maria Valentino (King's College London, United Kingdom): On the diagonalizability of the Atkin U-operator for Drinfeld cusp forms
Tuesday November 29th 2016, 17:00 - 18:15, Room F426
Abstract.
In this talk we shall begin with an introduction to the world of Drinfeld modular forms, which are the analogous of modular forms in the realm of function fields in positive characteristic. We shall then address the problem of the diagonalizability of the function field analogous of the Atkin U-operator. This is a joint work with A. Bandini (University of Parma).

• Mima Stanojkovski (Leiden University, Netherlands): Intense automorphisms of groups
Tuesday January 24th 2017, 17:00 - 18:15, Room F426
Abstract.
Let G be a finite group. A good strategy for understanding the structure of G is that of studying its group of symmetries, Aut(G). Let Int(G) be the subgroup of Aut(G) consisting of those automorphisms (called 'intense') that send each subgroup of G to a conjugate. Intense automorphisms arise naturally as solutions to a problem coming from Galois cohomology, still they give rise to a greatly entertaining theory on its own. We will discuss the case of groups of prime power order and we will see that, if G has prime power order but Int(G) does not, then the structure of G is (surprisingly!) almost completely determined by its nilpotency class.

• Sabrina Ouazzani (Université Paris-Est Créteil, France): A mixture of computability and ordinals, the infinite time Turing machines
Tuesday April 25th 2017, 17:00 - 18:15, Room F426
Abstract.
In this talk, we present infinite time Turing machines (ITTM), from a general introduction on computability and ordinals to the original definition of this transfinite model of computation. We will also present algorithmic techniques that allow to highlight some properties of the ITTM-computable ordinals. In particular, we will introduce gaps in ordinal computation times, that is to say, ordinal times at which no infinite time program halts.

• Martina Juhnke-Kubitzke (Universität Osnabrück, Germany): Face numbers of (balanced) simplicial polytopes and manifolds
Tuesday May 16th 2017, 17:00 - 18:15, Room F426
Abstract.
Given a closed manifold M together with a triangulation Δ, a classical question in geometric combinatorics and discrete geometry asks for the smallest number of vertices Δ can possibly have. Fixing the number of vertices, one can even wonder, what the smallest/largest number of edges are. More generally, a classical problem is to characterize all possible face numbers of Δ. The first part of this talk will provide a brief introduction into the study of face numbers of simplicial polytopes and manifolds and survey some of the most classical and important results. In the second part, we will consider so-called balanced triangulations, where a triangulation is balanced if and only if there exists a coloring of its vertices without monochromatic edges. In particular, we will be interested in lower bounds for the face numbers of this type of triangulations. This is joint work with Satoshi Murai, Isabella Novik and Connor Sawaske.

• Deirdre Haskell (McMaster University, Canada): Using model theory to find upper bounds on VC density
Tuesday May 30th 2017, 17:00 - 18:15, Room F426
Abstract.
The VC dimension of a collection of sets is a concept used in probability and learning theory. It is closely related to the model-theoretic concept of the independence property. In this talk, I will illustrate these concepts in various examples, and show how the model-theoretic approach can give some bounds on VC density. I will also talk a bit about my own experience as a woman in mathematics, and the place of affirmative action in hiring.

• Tobias Kuna (University of Reading, UK):Response theory for non-smooth observables and women in mathematics in the UK
Tuesday June 27th 2017, 17:00 - 18:15, Room F426
Abstract.
First, I will describe the situation of women in mathematics in UK with a particular focus on the national Athena SWAN (Scientific Women’s Academic Network) Charter and its effects. Then I will present a joint work with Viviane Baladi, who is a leading expert in the functional approach to statistical properties of dynamical systems. We studied together with Valerio Lucarini the change of the SRB measure of an Axiom A system with respect to the perturbation of the dynamic. The novelty is that we consider discontinuous observables which lead to linear or fractional response. The question is motivated by extreme value theory for dynamical systems and the associated over-threshold events.

• Malabika Pramanik (University of British Columbia, Canada): On Lebesgue-improving measures
Tuesday July 4th 2017, 17:00 - 18:15, Room F426
Abstract.
We know how to measure smoothness of a function (for example: how many times is it differentiable), but how does one measure the smoothness of a measure? This talk, intended for a general mathematical audience, will be devoted to a survey of this topic, with many examples. I will also talk a bit about my career path and some recent initiatives concerning women in mathematics that I have been involved with.

• Alev Topuzoglu (Sabanci University, Turkey) On permutation polynomials over finite fields
Tuesday July 18th 2017, 17:00 - 18:15, Room F426
Abstract.
Permutation polynomials over finite fields have gained considerable attention in the last decades, due to their vast applications, especially in combinatorics, coding and cryptography. In order to meet the specific requirements of individual applications, methods of construction of special types of permutations and/or new ways of classifying them are needed.
Carlitz rank of a permutation polynomial is a simple concept that was introduced in the last decade, and classifying permutations with respect to their Carlitz ranks was shown to have some significant advantages. This talk is intended for a general mathematical audience, and aims to present a variety of results concerning this notion. Based on my research experiences,  I will also include some suggestions for students and young researchers.

# KWIM Biennal Meetings

• KWIM-Tagung 2013, University of Konstanz, May 22nd, 2013.
• KWIM-Tagung 2015 , University of Konstanz, June 19th, 2015.
• KWIM-Festtage, University of Konstanz, December 6th-7th, 2018.

• # Other interesting links and upcoming international events

• Women in Mathematics Days 2018-19 - Expressions of Interest, deadline September 14th, 2018.
• Young Women in Mathematical Physics, September 24-26, 2018, University of Bonn, Germany.
• Optimization Days – Math Workshop for Female Master Students, October 4th, Trier, Germany.
• Women in Mathematical Material Science, November 5-6, 2018, Regensburg, Germany.
• German Chapter of European Women in Mathematics, Autumn 2019, Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany.
• Remembering Maryam Mirzakhani
• International Day of Women and Girls in Science: FEBRUARY 11th Read the Message from the Director-General of UNESCO , Ms Irina Bokova, on the occasion of the second celebration of this day and take a stand for girls and women in science by signing the Manifesto for Women in Science!

• Last update: 30.11.2018