Mathematik und Statistik
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Schwerpunkt Reelle Geometrie und Algebra > Prof. Dr. S. Kuhlmann > Mitarbeiter > Dr. L. Gregory

The mathematical modelling of Carbon Capture and Storage.

Mittwoch 10. Juli 17:00-18:30 Raum: P602
Madeleine Golding - University of Cambridge
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.

Solving cubics with paper and turtles

Dienstag 11. Juni 17:00-18:30 Raum: F420
Cythia Vinzant - University of Michigan
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.

Konstanz: Women in Maths

Am 22. Mai findet die Tagung "Konstanz: Women in Maths" in Raum K503 IBZ statt. Diese Tagung beginnt eine Reihe von Vorträgen zum Thema "Frauen in der Mathematik". Alle Mitglieder des Fachbereichs, insbesondere die Studierenden, sind herzlich eingeladen.
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, María 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

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 GNS construction

María Lopez Quijorna - Universität Konstanz
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.

Positive Polynomials and Sums of Squares

Charu Goel - Universität Konstanz
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".

Counting rational points on definable sets

Margaret Thomas- Universität Konstanz
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: 20. 05. 2013