Speaker:
Stefan Hollands

Coordinator:
Jörg Lehnert

Address:
Inselstraße 22
04103 Leipzig
Germany

Contact:
+49(0)341-9959-641
+49(0)341-9959-658
 IMPRS

Algebra and Geometry (AG)

Scientific Members working in this area

Current PhD Students

Surname, first nameEmailPhoneOfficeHomepage
Barth, LukasLukas.Barth572B3 08group
Camacho Cadena, FernandoFernando.Camacho830G2 02external
Freund, ValerieValerie.Freund666---- 
Hsiao, EnyaEnya.Hsiao830G2 02 
Koefler, JorisJoris.Koefler768F3 07external
Niemeyer, Merik JuljanMerik.Niemeyer831G2 03 
Shi, JiajunJiajun.Shi831G2 03 
Teich, MarieMarie.Teich539A3 10 
Zucal, GiulioGiulio.Zucal525A3 11 

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.

Alumni

NameAdvisorGraduationTopic
Zachary AdamsJürgen Jost2023Quasi-ergodicity of SPDE : spectral theory and phase reduction
Renan Assimos MartinsJürgen Jost2019The geometry of maximum principles and a Bernstein theorem in codimension 2 (see more)
David BauerMatthias Schwarz2013Towards discretization by piecewise pseudoholomorphic curves (see more)
Philipp BennerJürgen Jost2016Combining prior information for the prediction of transcription factor binding sites (see more)
Sarah BerkemerPeter F. Stadler2020Towards dynamic programming on generalized data structures and applications of dynamic programming in bioinformatics (see more)
Guy BussJürgen Jost2009On the construction and the behaviour of automorphic forms on completions of Teichmüller spaces and higher Bers maps
Brian ClarkeJürgen Jost2009The completion of the manifold of Riemannian metrics with respect to its L2 metric (see more)
Masud EhsaniJürgen Jost2021Self-organized criticality in neural networks by inhibitory and excitatory synaptic plasticity (see more)
Marzieh EidiJürgen Jost2022Topological and geometric methods with a view towards data analysis (see more)
Christoph EikemeierTobias Finis2022Asymptotics of Hecke operators for quasi-split simple groups (see more)
Vishal GuptaTobias Finis2018Limit multiplicity problem (see more)
Julian HofrichterJürgen Jost2014On the diffusion approximation of Wright-Fisher models with several Alleles and Loci and its geometry (see more)
Danijela HorakJürgen Jost2012Combinatorial Laplace operators on simplicial complexes
Leonhard HorstmeyerJürgen Jost2017Towards a geometric theory of exact lumpability (see more)
Shuhan JiangJürgen Jost2023Mathematical structures of cohomological field theories (see more)
Nidhi KaihnsaBernd Sturmfels2019Algebraic methods for dynamical systems and optimisation (see more)
Martin KellJürgen Jost2014On curvature conditions using Wasserstein spaces : with an application to the q-Laplace heat equation (see more)
Enno KeßlerJürgen Jost2017The super conformal action functional on super Riemann surfaces (see more)
Ilona KosiukJürgen Jost2012Relaxation oscillations in slow-fast systems beyond the standard form (see more)
Alexei LebedevJürgen Jost2008Simple modular Lie superalgebras
Shiping LiuJürgen Jost2012Synthetic notions of curvature and applications in graph theory (see more)
Arun MaitiHans-Bert Rademacher2017On the Goresky-Hingston product (see more)
Chiara MeroniRainer Sinn2022Semialgebraic convex bodies (see more)
Raffaella MulasJürgen Jost2020Spectra of normalized Laplace operators for graphs and hypergraphs (see more)
Wiktor MłynarskiJürgen Jost2015Functional sensory representations of natural stimuli : the case of spatial hearing (see more)
Wolfgang OttoPeter Stadler2011Transcriptional regulatory elements : detection and evolutionary analysis (see more)
Paolo PerroneJürgen Jost2018Categorical probability and stochastic dominance in metric spaces (see more)
Stephan PoppeJürgen Jost2017Foundational aspects of coherent predictive and statistical inference for exchangeable categorical sequences
Sharwin RezagholiJürgen Jost2020Hyperspace-type monads on top and the entropy theory of cynamical systems
Angel Eduardo Rodríguez FernándezPeter F. Stadler2021On the study of fitness landscapes and the Max-Cut problem (see more)
Christoph SachseJürgen Jost2007Global analytic approach to super Teichmüller spaces (see PDF)
Murat SağlamMatthias Schwarz2017A search for finer topological information by holomorphic curves in symplectizations : the case of lens spaces and their unit cotangent bundles
Camilo Eduardo Sarmiento CortésJürgen Jost2014Concerning triangulations of products of simplices (see more)
Mahsa Sayyary NaminBernd Sturmfels2021Real algebraic geometry of the sextic curves (see more)
Matti SchneiderMatthias Schwarz2013The Leray-Serre spectral sequence in Morse homology on Hilbert manifolds and in Floer homology on cotangent bundles (see more)
Gerardo Sosa GarciamarínJürgen Jost2017On symmetric transformations in metric measure geometry (see more)
Maximilian StegemeyerHans-Bert Rademacher2023On global properties of geodesics : the string topology coproduct and geodesic complexity (see more)
Linlin SunJürgen Jost2015Dirac equations, Dirac-harmonic maps and their heat flows
Tat Dat TranJürgen Jost2012Information geometry and the Wright-Fisher model of mathematical population genetics (see more)
Hanna TseranBernd Sturmfels, Guido Montúfar2023Expected complexity and gradients of deep maxout neural networks and implications to parameter initialization (see more)
José Javier VasquezHans-Bert Rademacher2017Isospectral nearly Kähler manifolds (see more)
Ying WangJürgen Jost2010Branching processes : optimization, variational characterization, and continuous approximation (see more)
Anatol WegnerJürgen Jost2015Subgraph covers : an information theoretic approach to motif analysis in networks (see more)
Ruijun WuJürgen Jost2017Analysis of a two-dimensional nonlinear sigma model with gravitino (see more)
Marius Emar YamakouJürgen Jost2018Weak-noise-induced phenomena in a slow-fast dynamical system
Odette Sylvia Yaptieu DjeungueJürgen Jost2018Generalizations of discrete Morse theory (see more)
Tinggui ZhangJürgen Jost2014Separability and local unitary equivalence of quantum states
Miaomiao ZhuJürgen Jost2008Harmonic maps and Dirac-Harmonic maps from degenerating surfaces
12.01.2024, 15:29