Faculty of Mathematics

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  • Department of Mathematics
    • Univ.-Prof. Goulnara Arzhantseva PhD

      Research Focus:
      Group Theory is one of the most fundamental domains of contemporary Mathematics. It is concerned with the study of 'groups', which are abstract representations of symmetries of mathematical objects. Group Theory plays a role in every branch of Pure and Applied Mathematics, and supplies powerful theoretical tools for solving problems in Physics, Chemistry, Information Science, and Engineering.

      The Geometric and Analytic Group Theory Research Team (GAGT Team) is at the forefront of the modern approach to the study of groups through analytic and geometric methods. These new methods have been extremely fruitful, and have led to the solution of several long-standing unsolved questions and opened new perspectives for further research. Analytic and Geometric Group Theory finds inspiration in methods from Analysis, Geometry, Combinatorics, Probability, Computer Networks, Crystallography, Quantum Mechanics, Relativity, and beyond. These methods are synthesized in an abstract framework to reveal the structure of groups. Conversely, the insights we gain by studying groups find application in these other domains. Analytic and Geometric Group Theory has become one of the main streams of Group Theory research, and is represented in major research centers worldwide. The GAGT Team, which started in Vienna in 2010, is the first research team in this field in Austria. Our current research interests include geometric, analytic, combinatorial, and computational aspects of group theory, low-dimensional topology, unitary representations and invariant measures, metric geometry, cryptography, complexity theory and randomization.

      More information can be found at:
      https://www.mat.univie.ac.at/~gagt/

    • Dipl.-Phys. Dr. Volker Branding, Privatdoz.

      Research Focus
      Differential Geometry, Geometric Analysis, Harmonic maps, Biharmonic Maps

      More information can be found at:
      https://www.mat.univie.ac.at/~branding/ 

    • Assoz. Prof. Mag. Dr. Roland Donninger

      Research Focus:
      Rigorous analysis of dispersive partial differential equations like nonlinear wave and Schrödinger equations, wave maps, in particular finite time blowup and long-time behavior

      More information can be found at:
      https://homepage.univie.ac.at/roland.donninger 

    • Univ.-Prof. Dr. Hans Georg Feichtinger

      Research Focus:
      I am working in Fourier Analysis and Function Spaces, specifically Gabor Analysis and Time-Frequency Analysis. In the past I have established the work-group NuHAG (with currently the members K. Gröchenig, M.Ehler, M.Dörfler, M Charina, J.L.Romero, P.Grohs), together with Prof. Gröchenig.
      We have published books in this area (1998,2001,2003), others in preparation.
      I have overall supervised ca. 8 Marie Curie Fellowships in the past, most of them pursuing now a good academic carreer: Massimo Fornasier (TU Muenich), Holger Rauhut (RWTH Aachen), Franz Luef (NTU Trondheim), S. Heineken (Buenos Aires), W.Czaja (College Park, MD, USA),... "  

      More information can be found at:
      www.nuhag.eu/hgfei 

      • Univ.-Prof. Bernhard Lamel, PhD

        Research Focus
        Several Complex Variables, in particular CR geometry

        More information can be found at
        complex.univie.ac.at 

      • Ass.-Prof. Yurii Malitskyi, PhD

        Research Focus
        Continuous optimization, application to machine learning

        More information can be found at:
        https://ymalitsky.com/  

      • Ass.-Prof. Mag. Dr. Angelika Manhart, BSc

        Research Focus
        Understanding cell biological phenomena using mathematical modelling. Methods include: modelling, analyising and simulating differential equations. The biological problems include: cell movemement, collective dynamics, cell cell organell scaling and behaviour.

        More information can be found at
        https://angelikamanhart.github.io/ 

      • Assoz.-Prof. Dr. José Luis Romero   

        Research Focus:
        Harmonic Analysis and Applications,
        Time-Frequency analysis,
        Stochastic point processes

        More information can be found at:
        https://sites.google.com/site/jlromeroresearch/ 

      • Univ.-Prof. Ulisse Stefanelli PhD
        Research group on Applied Mathematics and Modeling

        Research Focus:
        Calculus of variations and partial differential equations. Applications in mechanics and materials science.

        More information can be found at:
        https://www.mat.univie.ac.at/~stefanelli/         

      • Univ.-Prof. Balázs Szendroi, BA MAS PhD

        Research Focus:
        Pure mathematics: algebraic geometry, algebra and related areas.

        More information can be found at
        https://homepage.univie.ac.at/balazs.szendroi/  

      • Assoz. Prof. Vera Vértesi, Ph.D.

        Research Focus
        I am a researcher in low-dimensional topology, I have been working extensively with geometric, topological, and algebraic tools. My favourites include contact structures, Legendrian and transverse knots, braids, tangles, open books, singular foliations on surfaces, mapping class groups, Heegaard Floer homology, and TQFTs. My research primarily addresses classification and structural problems in contact 3-manifolds, along with the Legendrian and transverse knots they contain. I have proven the equivalence of the three Legendrian invariants in Heegaard Floer homology and classified Legendrian and transverse knots using Heegaard Floer homology, Legendrian contact homology, and convex surface theory. In a series of papers, I categorified the Reshetikhin-Turaev invariant for the Alexander polynomial by defining a Topological Quantum Field Theory for knot Floer homology. Together with J. Licata, I generalized open books for contact structures with boundary foliations and used this theory to define a glueable invariant of contact structures in bordered Floer homology. Most recently, we provided a proof for the Giroux correspondence, classifying contact structures via open book decompositions. Currently, I am working on several projects in 3- and higher-dimensional contact topology, as well as a project on lifting mapping classes via branched covering maps.

        More information can be found at
        www.mat.univie.ac.at/~vertesi/