Fachbereich Mathematik und Statistik |
Universität Konstanz |

Schwerpunkt Reelle Geometrie und Algebra > Prof. Dr. S. Kuhlmann > Dr. Charu Goel |

Die

- eine Vortragsreihe "Mathematikerinnen in Studium und Beruf",

- einen "Frauentreffpunkt Mathematik",

- eine "Beratung von Frauen für Frauen".

Dieses Projekt ist unterstützt durch den Gleichstellungsrat der Universität Konstanz von 01.05.2013 bis 30.04.2014 und weiter von 01.11.2014 bis 31.10.2015 mit der Projektnummer 674/12.

Auf dieser Seite finden Sie die Vorträge und die Veranstaltungen, die in dieser Vortragsreihe stattfinden werden. Ich koordiniere diese im Rahmen der Koordinationsstelle im Umfang von 25% TV-L 13.

- Tagung: Konstanz-Women in Mathematics, Universität Konstanz, 19. Juni 2015

- Teilnahme an anderen Veranstaltungen Frauen in der Mathematik:

--- The 16'th General meeting of EWM, Hausdorff Center for Mathematics in Bonn, September 2-6, 2013

--- Indian Women and Mathematics 2015, University of Delhi, April 2-4, 2015

--- European Women in Mathematics - German Chapter, Castle Rauischholzhausen, Marburg, April 30 - May 2, 2015

--- Women in Mathematics session: Ordered Algebraic Structures and Related Topics, CIRM, Luminy, Oktober 12 -16, 2015

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.

Im Mai 2013 ging durch die Medien (u.a. die New York Times), dass ein Durchbruch in Richtung Primzahlzwillingsvermutung erzielt wurde:Der zuvor unbekannte Mathematiker Y. Zhang konnte zeigen, dass die Folge der Primzahllücken $p_{n+1}-p_n$ unendlich oft einen endlichen Wert annimmt. Als obere Schranke für diesen Wert bewies er H=70.000.000, welche mittlerweise durch das Polymath8-Projekt auf H=246 gedrückt werden konnte. In dem Vortrag werde ich über die zugrundeliegende GPY-Methode und die Ideen, die zur Verbesserung der Schranke bis heute geführt haben, berichten.

A symmetric tensor is orthogonally decomposable if it can be written as a linear combination of tensor powers of n orthonormal vectors. Such tensors are interesting because their decomposition can be found efficiently. We study their spectral properties and give a formula for all of their eigenvectors. We also give equations defining all real symmetric orthogonally decomposable tensors. Analogously, we study nonsymmetric orthogonallydecomposable tensors, describing their singular vector tuples and giving polynomial equations that define them. In an attempt to extend the definition to a larger set of tensors, we define tight-frame decomposable tensors and study their properties.

I will outline the work I have been involved in, from my PhD years through to the present, to understand the properties and solution of several types of nonlinear PDEs, in particular the study of boundary value problems and of some specific geophysical fluid models. Almost all the PDEs I have studied model a time evolution process, all of them have been studied while juggling a busy family life and getting progressively more weighed down by administrative duties - another time evolution process!

I will review some basic properties about primes in non standard models of a weak fragment of Peano Arithmetic. I will then consider ideals of these structures and properties of the residue fields, and more in general of quotient fields.

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Simulation of hyperbolic flows in graph structures is challenging for several reasons. In this talk many of them are mentioned. One focus will be on the formulation as a Differential Algebraic System and why we really have to be careful on how to do it. The second focus will be on fast simulation of the discretized system. Fast simulation means Model Order Reduction Methods, but also time integration schemes.

We will consider the question where lies the boundary between decidability and undecidability in expansions of additive reducts of certain Euclidean rings, such as the ring of integers, polynomial rings or rings of formal power series over finite fields. In particular we will show how to use finite automata theory in order to get some decidability results in these expansions.

Model theory is a branch of mathematical logic with strong interactions with other branches of mathematics, including algebra, geometry and number theory. One of the objects of study of model theory are complete first-order theories and their classification. Shelah classified complete first-order theories by their ability to encode certain combinatorial configurations. For example the theories that are not able to encode linear orders are the stable theories. Shelah and others produced results and techniques for analyzing types and models in stable theories. In algebraic structures such as groups or fields, these model-theoretic properties are related with algebraic properties of the structure. Unfortunately, most structures studied in mathematics are not stable. Recently many of the tools used in stability theory could be generalized to larger classes of theories. This line of research is called "neo-stability theory". In this talk we will define the class of stable, NIP , simples and NTP2 and give some important examples.

Based on David Auburn's Pulitzer Prize-winning play of the same title and directed by John Madden, "Proof" brings on the big screen two Oscar prize winners Anthony Hopkins and Gwyneth Paltrow as mathematicians, father and daughter. It is an engaging story about the true authorship of a mathematical proof and the passions that coil around it.

The film is centered on a young female mathematician Catherine (Paltrow) haunted by the shadow of her father Robert (Hopkins), a brilliant mathematical genius but mentally unstable, that threatens her future. She was the only one to take care of her father over the years. On the eve of her twenty-seventh birthday she finds herself not only to cope with her sister Claire (Hope Davis), who does not share her life choices, but also with the attentions of Hal (Jake Gyllenhaal) a former student of her father. In this difficult context, Catherine fights to solve the most important question of her life: how much will she inherit of the madness of her father and how much of his genius?

The talk is closely related to a part of the book which I am writing together with Paulo Ribenboim. I will discuss the question how to approximate a fixed point of a strictly contracting mapping in an ultrametric space. The result will be applied to (Krull-) valued fields.

In this talk, we derive a priori error estimates for the finite element discretization of Dirichlet control problems with pointwise state constraints. The problem class is particularly challenging due to the low regularity of the states with L2-Dirichlet boundary controls. To obtain an optimality system of Karush-Kuhn-Tucker type with Lagrange multipliers for the pointwise state constraints prescribed in the interior of a 2D polygonal domain, we make use of higher interior regularity results for harmonic functions. Based on these results, finite element error estimates are derived with techniques that separate the regularity-limiting influences of the corners of the domain on the one hand, and the support of the Lagrange multiplier in the interior of the domain on the other hand. currently under investigation.

(joint work with Mariano Mateos)

Nach Cayley kann man jede spezielle orthogonale Matrix X, für welche det(1+X) nicht gleich als 0 ist, in der Gestalt X=(1+Y)^{-1}(1+Y) mit schiefsymmetrischem Y schreiben. Auf diese Weise erhält man eine Parameterdarstellung

{schiefsymmetrische Matritzen} --> SO(n,R) \ {det(1+X)=0}

Dies lässt sich mit geringen Modifikationen verallgemeinern auf beliebige (nicht ausgeartete) quadratische Formen über beliebigen Köpern der Charakteristik nicht gleich als 2. Hauptinhalt des Vortrags ist, mit Hilfe dieser Parameterdarstellung eine invariante Differentialform höchsten Grades auf den speziellen orthogonalen Gruppen explizit anzugeben. Motiviert wird das durch den Wunsch, das Tamagawa-Mass auf der Adelgrupe G_A einer speziellen orthogonalen Gruppe G über Q zu beschreiben (und zu benutzen). Hierzu benötigt man Masse auf den Komplettierungen G_{Q_v}, die alle von derselben über Q definieren Differentialform kommen.

Emmy Noether (1882-1935) ist eine der wichtigsten Figuren in der Mathematik ihrer Zeit und gilt als der bisher bedeutendste Mathematiker weiblichen Geschlechtes. Zugleich lebt sie in einer Zeit, wo ihr Geschlecht, ihr linksliberaler Pazifismus und ihr jüdischer Hintergrund zu existentiellen Hindernissen werden. Die Synthese dieser beiden Fakten macht sie zu einer faszinierenden Person, nach der nicht nur mathematische Begriffe, sondern auch viele Preise, Programme, Ehrungen etc. bezeichnet werden. Der Vortrag will einige Facetten ihres Lebens und Schaffens streifen.

Material flow systems are usually divided into a microscopic and a macroscopic model scale. On the one hand macroscopic flow models are used for large scale simulations with a large number of parts. On the other hand microscopic models are needed to describe the details of the production process. We present an overview of models for material flow problems ranging from detailed microscopic models to macroscopic models based on conservation laws. Numerical simulations are presented on all levels of the hierarchy and validated against real-data test settings. The investigation of optimal control problems arising in this context is also discussed.

Particulate processes involving handling of solids is ubiquitous in various industries and is typically operated inefficiently due to a lack of adequate mechanistic process understanding. One of the primary application of such processes is found in the pharmaceutical industry involving manufacturing of solid dosage forms (e.g. tablets). This work focuses on improved mathematical modeling of such particulate processes using the population balance modeling framework. One of the primary objectives deal with model development for granulation followed by development of improved numerical techniques for reduced computational overheads associated with the solution techniques for solving population balance models. The insights from this work is believed to make a significant contribution towards improved understanding of the particulate processes and the current inefficient operation of the downstream manufacturing process can be mitigated. This work is highly multi-disciplinary and successfully combines concepts from various spheres of science, mathematics and engineering.

Groups with a chain condition on centralizers (MC groups) have been studied by Bryant in the 70's. He proved, that the Fitting group (the subgroup generated by all normal nilpotent subgroups) of a periodic MC-group is always nilpotent. On the other hand, such groups appear naturally in the model theoretic context as stable groups form a subclass of MC-groups. Using model theoretic instruments, Wagner generalized this result to stable groups and later together with Derakhshan to any MC-group. Independent of these results, Altinel and Baginski have shown that any nilpotent subgroup of an MC-group has a definable envelope which has the same nilpotency class. In our talk we introduce groups with a chain condition on centralizers up to finite index, which we call approximate MC-groups. Again, these groups appears naturally in the field of model theory, i.e. any group with a simple theory is an approximately MC-group. In this context, Milliet showed that any abelian, soluble or nilpotent group is contained in a definable finite-by-abelian, finite-by-soluble or finite-by-nilpotent subgroup. Recently, Wagner proved that in fact the Fitting group of any simple group is nilpotent.

The first part of the talk is devoted to the life of Olga Taussky-Todd, a great mathematician, wonderful teacher and nice woman who was born in 1906 in Olmütz (Austro-Hungarian Empire), and who died in 1995 in Pasadena (California, USA). She was mainly interested in Number Theory and Matrix Theory but she also wrote a famous paper on "Sums of Squares" and participated to the edition of Hilbert's collected works in Number Theory while she was in Göttigen.

The second part of the talk is colloquium style and devoted to Hilbert's 17th problem - a problem related with sums of squares - and presents how this old Hilbert's problem has been a source for several new developments and research areas.

`Convolution surfaces' refer to a geometric modeling technique used in computer graphics to generate smooth 3D volumes around a skeleton of lower dimension. One-dimensional skeletons create tubular like volumes which are well suited for modeling organic shapes. For general shapes one needs to consider 2D skeletons as well. The surfaces bounding the shapes are defined as level set of a function obtained by integrating a kernel function along this skeleton. To allow for interactive modeling, the technique has relied on closed form formulae for integration obtained through symbolic computation software. With a background in symbolic computation, I got involved in this subject when Marie-Paule Cani (INRIA Grenoble) challenged me to obtain new formulae, for a wider range of basic skeletons. Taking a dive in the Computer Graphics literature and organising the mathematics to be used for the code has been a rather refreshing and satisfying experience.

From Hilbert Nullstellensatz for the ring of complex polynomial, we go to rings of germs of holomorphic functions, then to the ring of real polynomials and the ring of real analytic germs. We discuss the difficulties which arise passing from local to global analytic set and we come to the solution given by O.Forster for Stein algebras.

Finally we discuss a recently proved real global analytic Nustellensatz.

In the present talk, we investigate the impact of non-Markov parameters on the stability of a finite-dimensional dynamical system. The consideration is given both to the case of continuous and discrete processes. First, we obtain moment equations for different classes of differential equations with random coefficients and random transformations of solutions. Then we present necessary and sufficient conditions for L_2-stability of solutions for these classes of dynamical systems. We further apply the Lyapunov functional method to systems of non-linear differential and difference equations with right-hand part depending on a semi-Markov process. A construction of the Lyapunov functions through moment equations for stochastic equations is performed. Finally, necessary and sufficient conditions for the L_2-stability of solutions with random influence are deduced based on Lyapunov functions.

It was the Hungarian mathematician Josef Kuerschak who gave the formal definition of an absolute value during the Cambridge International Congress of Mathematicians in 1912. The motivation for this was Hensel's work on the field of p-adic numbers. According to Kuerschak, the notion of an absolute value of a field K is a generalization of the notion of ordinary absolute value of the field of complex numbers. The development of the theory of absolute values gained momentum by the discovery of the fact that much of algebraic number theory can be better understood by using absolute values. We go down the memory lane and discuss some significant contribution to this theory by Kuerschak, Ostrowski, Hasse, Artin and others.

There are many voting methods in use around the world and we ask the question: Which voting method is best in the sense of best reflecting the "will of the voters". It turns out that mathematics can help answer the question! In the 1950's, Kenneth Arrow proved a theorem that implies if there are more than two candidates in an election, here is NO good way to choose a winner in the sense that it is always possible that a "bad" outcome can occur. In this talk we will discuss Social Choice Theory, a mathematical model of voting, and Arrow's Theorem. We will see some examples that show that paradoxes and bad outcomes can and do happen in real life elections. We discuss some recent joint work with M. Castle connecting pairwise tallies in an election with election outcomes in some election methods. This work generalizes work of D. Saari and T. McIntee. No previous knowledge of Social Choice Theory is assumed.

The talk will present the aim and activities or two regional organizations for women in mathematics I am involved in. EWM, European Women in Mathematics is an international association of women working in the field of mathematics in Europe. Founded in 1986, EWM has several hundred members and coordinators in over 30 European countries. Every other year, EWM holds a general meeting and a summer school. A newsletter is published at least twice a year, EWM has a website and an e-mail network. AWMA, African Women in Mathematics Association was founded in 2013 in South Africa after a first workshop in Burkina Faso in 2012. Another workshop will be organized in Kenya in 2015.

References

EWM website http://www.europeanwomeninmaths.org/

AWMA http://www.europeanwomeninmaths.org/resources/news/creation-awma-african-women-in-mathematics-association

Everyone will agree that one can decompose a solid unit ball in three-dimensional space into finitely many disjoint subsets which one can in turn put together in a different way yielding two solid unit balls if one is allowed to stretch the pieces. The Banach-Tarski paradox states that this is also possible performing only rotations and translations. This seems to be counter-intuitive since the volume is rotation and translation invariant. We will see how this problem is solved by looking at the construction of a paradoxical decomposition of the unit ball which uses some group actions on the sphere and the axiom of choice.

Der Kosmos und seine Gesetze haben die Menschen seit jeher fasziniert. Viele Wissenschaftler und Philosophen haben versucht zu beschreiben und zu erklären, was sie am Himmel sahen. Und fast alle von ihnen haben Mathematik verwendet, um ihre Ideen darzustellen und Vorhersagen für die Zukunft zu treffen. In der heutigen Zeit verstehen wir sehr viel besser, wie sich Planeten, Sterne und Galaxien verhalten. Und immer noch nutzen wir die Mathematik als Sprache, in der wir die Geheimnisse unseres Universums formulieren und zu lüften versuchen.

In dem Vortrag werden wir uns mit Isaac Newton (1643-1727) und Albert Einstein (1879-1955), zwei der berühmtesten Physiker aller Zeiten, und ihren Theorien über unser Universum beschäftigen. Wir werden Gemeinsamkeiten und Unterschiede ihrer Sichtweisen diskutieren sowie die Mathematik untersuchen, die sie zur Formulierung ihrer Theorien verwendet haben. Unterwegs werden wir auch den berühmten Mathematiker Carl Friedrich Gauß (1777- 1855) und seine wunderschoönen Einsichten zur Krümmung kennenlernen.

The Keller-Segel model is a classical model for cell motion and aggregation due to chemotaxis. In this talk a related model with a non-diffusing chemical is described and analyzed, which behaves "more" hyperbolic.

Further, pattern formation in a model for the reorientation of cells due to direct cell-cell contact is discussed. An interesting question in this context is, if periodic traveling wave patterns can occur, which are observed in biological experiments.

It is often tougher for a woman to become a mathematician than it is for a man, especially in some parts of the world where the few women who make their way up in the academia as a mathematician are therefore remarkable women. As a woman mathematician, I have had the chance to meet various women mathematicians around the world who have impressed me beyond mathematics, as human beings. I would like to report here (with the protagonists' approval and without claiming any objectivity) about the scientific trajectories of some of them and the joys or difficulties they encountered in their careers as women mathematicians. Based on these portraits I hope to discuss the impact of the social environment and prejudices on women's careers as mathematicians.

The moment problem is a fundamental problem of fairly old origin, that is still a source of many open questions within pure mathematics as well as numerous applied fields. The purpose of this talk is to give an introduction to the moment problem, exploring some recent results in finite and infinite dimensions. The question addressed by the K-moment problem is to characterize all possible moment sequences of Borel measures which are supported on a given closed subset K of a certain space X. For instance, in the classical setting, the moment problem asks whether there exists a probability measure on the real line having specified mean, variance and so on. We start our journey with X=|R^d, particularly focusing on the case when K is a basic semi-algebraic set, namely a subset given by polynomial constraints. On our way, we develop some aspects of the duality between moments and sums of squares of polynomials (s.o.s.), as well as the relationship between nonnegative polynomials and s.o.s.. We naturally end up in the case when X is an infinite- dimensional space. In particular, we present a recent generalization of the previous results in finite dimensions for the moment problem on a closed semi-algebraic subset of the space of generalized functions. This result has been strongly inspired by applications related to the analysis of many-body systems, e.g. in statistical mechanics, spatial ecology, etc.

Consistent with the stereotype that females are more anxious and less capable in mathematics than males, women are still under-represented in math-intensive occupations. In the talk, findings from studies will be presented, which were conducted to examine gender differences in trait (habitual) versus state (momentary) mathematics anxiety in a sample of students. For trait math anxiety, the findings of the studies replicated previous research showing that female students report higher levels of anxiety than do male students. However, no gender differences were observed for state anxiety, as assessed using experience-sampling methods while students took a math test and attended math classes. These findings thus suggest that girls do not actually experience more math anxiety than boys in the classroom, with gender differences being observed only on generalized assessments that permit bias due to gender stereotypes. The possible role that stereotyped beliefs regarding math ability play with regard to women not choosing to pursue careers in math-intensive domains are discussed.

A one-hour biographical documentary, that tells the story of an important American mathematician against a background of mathematical ideas. Julia Robinson, a pioneer among American women in mathematics, rose to prominence in a field where often she was the only woman. Julia Robinson was the first woman elected to the mathematical section of the National Academy of Sciences, and the first woman to become president of the American Mathematical Society. Her work, and the exciting story of the path that led to the solution of Hilbert's tenth problem in 1970, produced an unusual friendship between Russian and American colleagues at the height of the cold war. In this film, Robinson's major contribution to the solution of H10 triggers a tour of 20th century mathematics that moves from Paris in 1900, through the United States, to the Soviet Union and back. Following the passionate pursuit of an unsolved problem by several individuals in different countries adds to the emotional intensity of the mathematical quest.

The film covers important events in the history of modern mathematics while conveying the motivations of mathematicians, and exploring the relationship between mathematical research and the development of computers.

Carbon Capture and Storage is a way of reducing the emissions of carbon dioxide (CO2) from human activity and thus helping to mitigate climate change. Carbon dioxide is captured from a fixed source such as a large coal-fired power station so that it is not released into the atmosphere. The gas can then be compressed and transported to a suitable storage site, such as a deep underground rock formation. The CO2 is injected about a kilometre underground into rock that is saturated with salt water. We can use mathematics to better understand and predict what happens next!

During this talk I will explain how we can use mathematical tools, including partial differential equations, to model the physical processes which occur as the carbon dioxide moves through the rock deep underground. Do come along to find out about this exciting application of mathematics which I studied for my PhD. The theory can be verified and illustrated by laboratory experiments using just a fish tank filled with sand, as well as data from actual storage sites currently in operation and all of this will be included in the talk.

What is the mathematics behind origami? What can be achieved by just folding paper? I'll talk about the beautiful geometry underlying these questions and more, including a classical algorithm for solving polynomials with a turtle and (more modern) algorithm for solving cubic polynomials with a piece of paper.

Die Tagung wird durch den Gleichstellungsrat der Universität Konstanz finanziert.

9:00-9:15 | Welcome |

9:15-10:00 | Counting rational points on definable sets, Margaret Thomas, Universität Konstanz |

10:10-10:55 | Algebra from a computable perspective, Karen Lange, Wellesley College |

11:00-11:30 | Kaffee |

11:30-12:15 | Exponential polynomials and their roots, Paola D'Aquino, Seconda Università degli Studi di Napoli |

12:30-13:00 | The truncated GNS construction, Maria Lopez Quijorna, Universität Konstanz |

13:00-14:30 | Mittagspause |

14:30-15:00 | Positive Polynomials and Sums of Squares, Charu Goel, Universität Konstanz |

15:10-15:55 | Die Doktorarbeit, die Universität und der ganze Rest - wie ich mich dazu entschied zu promovieren und was ich seit dem tue, Katharina Dupont, Universität Konstanz |

Vielen NichtmathematikerInnen, aber auch Studierenden der Mathematik, fällt es schwer sich vorzustellen, was man macht, wenn man eine Doktorarbeit im Fach Mathematik schreibt. In meinem Vortrag werde ich einen Eindruck davon zu vermitteln, was es bedeuten kann zu promovieren. Dabei werde ich ganz persönlich darüber berichten, wie ich bestimmte Situationen empfunden habe. Auch darüber was mir bei der Entscheidung zu promovieren geholfen hat, werde ich berichten. Bei einem "Frauen in der Mathematik Tag" stellt sich natürlich auch die Frage, in welchen Situationen es eine Rolle spielt eine Frau zu sein, oder ob das nicht eigentlich völlig egal ist.

The truncated moment problem asks for the characterization of the linear forms L\in|R[x]*_2t, t\in |N, having a representing measure. In this presentation we start with a given linear form, and with the new point of view of the truncated GNS operators, we will try to decide if such a linear form comes from a measure, and in this case we will try to find the support of such a measure.

In 1888 Hilbert proved that P_{n,m} = S_{n,m} iff n = 2,m = 2, or (n,m) = (3,4), where P_{n,m} and S_{n,m} are respectively the cones of positive semidefinite (psd) and sum of squares (sos) real forms of degree m in n variables. Thus in all other cases S_{n,m} is strictly contained in P_{n,m} (I will call them non-Hilbert cases). I will start by surveying known tests on the coefficients of a form to be sos and further results by Choi, Lam, Reznick and Harris relating even symmetric psd and sos forms in some of the non-Hilbert cases. Then I will introduce our problem: "Finding tests on the coefficients of a symmetric or even symmetric form to be psd or sos", and present a relevant worked out example. Finally I will present the main question that I work on, i.e. "Filtration of intermediate cones between sos and psd cone".

The problem of counting the number of rational points (tuples all of whose coordinates are rational numbers) lying on subsets of Euclidean space is one which has interested number theorists for more than a hundred years, in particular where the sets are "algebraic". In the analogous "transcendental" case (these ideas for sets are analogous to the definitions of algebraic and transcendental numbers), progress has happened only relatively recently. In particular, a breakthrough was made in 2006 by Pila and Wilkie, who considered just those subsets of the real numbers which can be thought of as definable in certain structures (in the sense of first order logic). They proved a strong (i.e. low) upper bound for the number of rational points on those sets. We will look at some of the work on this topic that lead up to their result and try to describe some of the methods they used in proving it.

Letzte Änderung: 12. 11. 2015