Institutskolloquium – SS 2016

Das Institutskolloquium findet während der Vorlesungszeit an jedem Donnerstag um 17:15 Uhr im Raum 05-432 (Hilbertraum) statt. Ab 16:45 Uhr gibt es Kaffee und Kuchen.

Anlässlich des 300. Todestages von Gottfried Wilhelm Leibniz veranstaltet das Institut für Mathematik im Sommersemester 2016 gemeinsam mit der Hochschule für Musik eine Vortragsreihe "Zahl und Klang" zum Thema Leibniz und die Musik.

Außer der Eröffnungsveranstaltung am 18.04.2016, 19:00 Uhr, im Großen Haus des Staatstheaters Mainz finden die weiteren Vorträge aus dieser Reihe jeweils Donnerstags zu den üblichen Terminen des Institutskolloquiums statt. Bitte beachten Sie jedoch die abweichenden Zeiten und Räume!

18.04.2016 19:00 Uhr Eröffnung "Zahl und Klang", Staatstheater Mainz | Großes Haus
Leibniz und Newton: Die Anfänge der Infinitesimalrechnung (Prof. Dr. Manfred Lehn)
Bigband der Hochschule für Musik mit Songs von Frank Sinatra (Leitung: Jiggs Whigham, Gesang: Alexander Gelhausen)

21.04.2016 17:00 Uhr c.t. N.N.

28.04.2016 19:30 Uhr Hochschule für Musik | Roter Saal
Zahlen und Zahlsysteme (Prof. Dr. Manuel Blickle)
Claviersysteme (Leitung: Prof. Dr. Immanuel Ott, Prof. Dr. Birger Petersen)

12.05.2016 19:30 Uhr Hochschule für Musik | Roter Saal
Leibniz und Logik (Prof. Dr. Steffen Fröhlich)
Johann Sebastian Bach: Chaconne aus der Partita Nr. 2 d-moll BWV 1004 (Leitung: Prof. Dr. Felix Koch)

18.05. - 20.05.2016 Festkolloquium zu Ehren von David E. Rowe

02.06.2016 18:30 Uhr JGU | Linke Aula
Ordentlich denken. Musik als Mathematik in der Geschichte der Philosophie (Prof. Dr. Dr. Stefan Seit)
Musikalische Fragmente - Gregorianischer Choral aus württembergischen Klöstern (Leitung: Prof. Dr. Stefan Morent, Musikwiss. Institut Universität Tübingen)

09.06.2016 17:00 Uhr c.t. Prof. Dr. Bastian von Harrach (Goethe-Universität Frankfurt)
Inverse problems and medical imaging

Abstract: Medical diagnosis has been revolutionized by noninvasive imaging methods such as computerized tomography (CT) and magnetic resonance imaging (MRI). These great technologies are based on mathematics. If the patient's interior was known then we could numerically simulate the outcome of physical measurements performed on the patient. Medical imaging requires solving the corresponding inverse problem of determining the patient's interior from the performed measurements.

In this talk, we will give an introduction to inverse problems in medical imaging, and discuss the mathematical challenges in newly emerging techniques such as electrical impedance tomography (EIT), where electrical currents are driven through a patient to image its interior.

EIT leads to the inverse problem of determining the coefficient in a partial differential equation from (partial) knowledge of its solutions.

We will describe recent mathematical advances on this problem that are based on monotonicity relations with respect to matrix definiteness and the concept of localized potentials.

16.06.2016 19:30 Uhr Hochschule für Musik | Roter Saal
Die Leibnizsche Rechenmaschine (PD Dr. Ulf Hashagen)
Musikautomaten (Leitung: Prof. Dr. Peter Kiefer)

23.06.2016 17:00 Uhr c.t. N.N.

30.06.2016 19:30 Uhr Hochschule für Musik | Orgelsaal
Doppelbrechung - Leibniz und Huygens (Prof. Dr. Duco van Straten)
Orgel und Stimmungssysteme (Leitung: Prof. Dr. Gerhard Gnann, Prof. Hans-Jürgen Kaiser)

07.07.2016 17:00 Uhr c.t. Prof. Dr. Christine Proust (Laboratoire SPHERE, SAW project - CNRS & Univ. Paris Diderot)
Numbers, quantities and magnitudes in mathematical cuneiform texts: historiographical and historical approaches

Abstract: What are numbers, quantities and magnitudes in the context of texts written more than 4000 years ago, such as mathematical cuneiform texts? We recognize these notions in ancient texts, and in a way, they appear to us as quite familiar. However, a close analysis of the way in which ancient scribes worked with numbers and quantities allows to grasp a variety of unexpected practices. The concepts shaped by the ancient actors differ from the rather uniform meaning we give to the words "numbers", "quantities" and "magnitudes" today.

In this talk, I first offer a broad overview of the mathematical cuneiform texts that have come down to us. Then, I analyze how the pioneers of the studies of cuneiform mathematics, Otto Neugebauer and François Thureau-Dangin, and their heirs understood the notions of numbers, quantities and magnitudes as evidenced by ancient texts. Finally, I suggest a completely different approach, based on elementary school texts found in southern Mesopotamia and dated to the early second millennium BCE. I show how the pedagogical intentions perceptible in school texts shed light on the native understandings of numbers, quantities and magnitudes, and induce new interpretations of scholarly mathematical texts. Indeed, focusing on native conceptions of numbers and quantities is a way to approach and understand the originality of the mathematical content of scholarly texts. The arguments will be grounded on a detailed presentation of a selection of school and scholarly texts. I will focus particularly on the calculations with floating sexagesimal place value numbers.

14.07.2016 17:00 Uhr c.t. N.N.

21.07.2016 17:00 Uhr c.t. Jun.Prof. Dr. Sabine Jansen (Ruhr-Universität Bochum)
Multi-species virial expansions

Abstract: Condensation and nucleation is often modelled with the Becker-Döring equations, a coupled system of ordinary differential equations that describes a coagulation-fragmentation process of droplets of different sizes. For simple forms of ODE coefficients, explicit Lyapunov functionals have been given, but there is some debate about what the "correct" coefficients are. Equilibrium statistical mechanics suggests Lyapunov functionals should be free energies, i.e., rate functions of appropriate large deviations principles from probability. Free energies are notoriously hard to compute and often represented as power series.

I will present a convergence result for the free energy of a mixture of countably different types of particles (e.g. droplets of different sizes). The result is based on cluster expansions and the multi-variate Lagrange-Good inversion, a tool that also has applications to generating functions, branching processes, and analytic combinatorics. The talk is based on joint work with Stephen Tate, Dimitrios Tsagkarogiannis and Daniel Ueltschi (Comm. Math. Phys. 2014).