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Algebra and Geometry (AG)

Description of Research

Algebraic Geometry.

This is the study of solution sets to polynomial equations in several variables. If the variables range over the real numbers, then one speaks of real algebraic geometry, which is a subject with many applications, e.g., in optimization and statistics.

Lie Groups and Number Theory.

Number theory is a central field in mathematics, with ramifications in logic, algebra, and algebraic geometry. In this context, we study automorphic forms and their relations to representations of Lie groups over fields of an arithmetic nature. This stands in contrast to the appearance of Lie groups in the study of homogeneous spaces, particularly in higher Teichmüller theory, which is also studied in this working group.

Differential and Symplectic Geometry.

The strong geometry division at the IMPRS covers Riemannian geometry, complex geometry, and symplectic geometry. Riemannian geometry enters the classification problems for black holes, rigidity results, or the geometric analysis of initial data sets. Symplectic geometry underpins all of classical mechanics. In some cases, symplectic automorphisms describe the evolution of physical systems. Such systems exhibit both a generic tendency for chaotic behavior as well as rigidity in the Hamiltonian case. At the intersection of complex geometry and complex dynamics, one studies holomorphic foliations and rigidity results for manifolds admitting a Levi foliation.

Combinatorics.

It has been said that combinatorics is the nanotechnology of mathematics. The term is sometimes used synonymously with "discrete mathematics". This field is closely connected with computer science. Local expertise includes geometric combinatorics and polyhedral algorithms, graphs, hypergraphs and their applications, and tropical combinatorics and their connection to computer algebra.

Data and Computation.

Recent years have seen explosive development in data science. Mathematics plays an important double role: it provides method for analyzing data, but it also generates interesting data in its own right. Mathematical software packages play a significant role here. Data analysis that uses various innovative approaches from geometry and topology to make sense of high-dimensional data is studied in our IMPRS.

Scientific Members working in this area

Current PhD Students

Alumni

The graduates are organized alphabetically by last name. To make navigation easier for you, you can either select the initial letter directly or use the year selection to display all entries from a specific year. Additionally, you will find the title, advisor, and graduation year here. If you would like more information about a particular work, simply click on the title of the thesis.

B

Buss, Guy

On the construction and the behaviour of automorphic forms on completions of Teichmüller spaces and higher Bers maps Jürgen Jost 2009
D

di Dio, Philipp J.

The truncated moment problem Konrad Schmüdgen 2018

Dubray, David

F

Fevola, Claudia

Computation and physics in algebraic geometry Bernd Sturmfels, Daniele Agostini 2023
G

Görlach, Paul

Projective geometry, toric algebra and tropical computations Bernd Sturmfels, Mateusz Michalek 2020

Große, Nadine

Gupta, Vishal

Limit multiplicity problem Tobias Finis 2018
I

Izadi Khaleghabadi, Mohammad

L

Lebedev, Alexei

Simple modular Lie superalgebras Jürgen Jost 2008

Long, Yangjing

M

Maiti, Arun

On the Goresky-Hingston product Hans-Bert Rademacher 2017

Marigliano, Orlando

Meroni, Chiara

Semialgebraic convex bodies Rainer Sinn 2022

Mintas, Fatmagül

Twistor spinors on Riemannian spin orbifolds Hans-Bert Rademacher 2009
N

Nitsche, Max Joachim

Zur Eisenbud-Goto-Vermutung für affine Halbgruppenringe Jürgen Stückrad 2012
P

Poppe, Stephan

Foundational aspects of coherent predictive and statistical inference for exchangeable categorical sequences Jürgen Jost 2017
R

Rezagholi, Sharwin

Hyperspace-type monads on top and the entropy theory of cynamical systems Jürgen Jost 2020

Rodríguez Fernández, Angel Eduardo

Roncoroni, Lavinia

S

Sachse, Christoph

Sağlam, Murat

A search for finer topological information by holomorphic curves in symplectizations : the case of lens spaces and their unit cotangent bundles Matthias Schwarz 2017

Sarmiento Cortés, Camilo Eduardo

Savchuk, Yurii

Unbounded induced *-representations Konrad Schmüdgen 2008

Sayyary Namin, Mahsa

Seynnaeve, Tim

Sosa Garciamarín, Gerardo

Sun, Linlin

Dirac equations, Dirac-harmonic maps and their heat flows Jürgen Jost 2015
V

Vasquez, José Javier

Isospectral nearly Kähler manifolds Hans-Bert Rademacher 2017

Vodička, Martin

Y

Yamakou, Marius Emar

Weak-noise-induced phenomena in a slow-fast dynamical system Jürgen Jost 2018

Yaptieu Djeungue, Odette Sylvia

Z

Zhang, Tinggui

Separability and local unitary equivalence of quantum states Jürgen Jost 2014

Zhu, Miaomiao

Harmonic maps and Dirac-Harmonic maps from degenerating surfaces Jürgen Jost 2008