Office hours (virtual) as Dean of Studies

Every Monday, 16:00-18:00, no registration necessary, via BigBlueButton

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CURRENT TEACHING (SS 26)

• VO+PS Introduction to Higher Algebra (Algebraic Geometry)
• SE Forschungsseminar Operator Systems
• SE MIP-Seminar

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LECTURE NOTES

• Lineare Algebra (video lectures can be found here)
• Algebra
• Algebraic Geometry
• Real Algebra and Geometry
• Operator Algebra
• Algebraic Topology

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PHD PROJECTS

• Projections to Classical and Free Convex Sets
  Maximilian Illmer, ongoing
• Minimal Operator Systems
  Markus Dannemüller, ongoing
• Positive and Invariant Tensor Decompositions: Approximations and Applications
  Andreas Klingler, completed in September 2024 (with Gemma De les Coves)
• Where Convex Cones Meet Tensor Products: A Dimension Free Perspective
  Mirte van der Eyden, completed in June 2024 (with Gemma De les Coves)
• On the Free Carathéodory Number and Operator Systems over the Cone of Positive Semidefinite Matrices
  Martin Berger, completed in November 2022
• Approximation Techniques for Positive Matrices
  Paria Abbasi, completed in February 2022
• Stability of Non-Commutative Quadratic Modules
  Philipp Jukic, completed in March 2020
• Free Convex Semi-Algebraic Geometry - The Limits of Quantifier Elimination, Projection Properties, and Operator Systems
  Tom Drescher, completed in September 2018

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MASTER PROJECTS

• Curriculare Kohärenz und mathematische Kompetenzentwicklung (LA)
  Sara Lechner, ongoing (with Surette Van Staden)
• Homotopy Methods in Optimization
  Noah Kleinschmidt, ongoing
• Summen von zwei Quadraten (LA)
  Matthias Unterkirchner, ongoing
• Die Sätze von Radon und Helly (LA)
  Angelika Moser, ongoing
• Pseudozufallszahlen (LA)
  Mathias Zerlauth, ongoing
• Der Freundschaftssatz (LA)
  Michael Walter, Summer Term 2025
• On Barker's Conjecture
  Jasmin Matti, Summer Term 2025
• Sandpile Groups
  Julia Überbacher, Summer Term 2025 (with Ecaterina Sava-Huss)
• K-Theory for Operator Algebras
  Maximilian Illmer, Summer Term 2024
• Guarding a Museum (LA)
  Lisa Giner, Summer Term 2024
• On Quantum Random Walks
  Andreas Mair, Winter Term 2023/24 (with Ecaterina Sava-Huss)
• Geometry of (Joint) Numerical Ranges
  Beatrice Maier, Winter Term 2023/24
• Completing Latin and Quantum Latin Squares
  Wolfgang Wetscher, Summer Term 2023
• Das Lösen von linearen Gleichungssystemen über kommutativen Ringen (LA)
  Maria Wurzer, Summer Term 2023
• Wie findet oder zählt man Nullstellen? (LA)
  Diana Held, Summer Term 2022
• Quantum Generalizations of Magic Squares and Latin Squares
  Inga Valentiner-Branth, Winter Term 2021/22 (with Gemma De las Cuevas)
• Primzahlen und ihre Bedeutung in der Kryptographie (LA)
  Daniela Aichner, Winter Term 2021/22
• Quantifier Elimination in Matrix Rings
  Clemens Brüser, Winter Term 2021/22
• Free Separation and Entanglement Witnesses
  Ralph Gorbach, Summer Term 2021
• Decidability of Algebra-valued Tensor Networks
  Joshua Graf, Summer Term 2021 (with Gemma De las Cuevas)
• Von den rationalen Zahlen zur Nichtstandardanalysis (LA)
  Matthias Knapp, Winter Term 2020/21
• Der Eulersche Polyedersatz (LA)
  Iacun Maria Prugger, Winter Term 2020/21
• On the Free Separation Theorem
  Manuel Astner, Winter Term 2020/21
• Axiomatische Geometrie (LA)
  Iris Wohlgemuth, Summer Term 2020
• Knotentheorie (LA)
  Jasmina Massoudy, Summer Term 2020
• Gewöhnliche homogene lineare Differenzengleichungen erster und zweiter Ordnung mit konstanten Koeffizienten (LA)
  Nadja Hofer, Summer Term 2020
• Das Lemma von Sperner: Anwendung und Schulbezug (LA)
  Magdalena Berger, Summer Term 2020
• Sphärische Geometrie im Schulunterricht (LA)
  Franz Gänsluckner, Winter Term 2019/20
• Quantitative Aspects of Polytopes and Spectrahedra
  Johanna Lercher, Summer Term 2019
• Kryptographie im Schulunterricht (LA)
  Aygül Koc, Summer Term 2019
• Freie Polytope und Polyeder
  Beatrix Huber, Summer Term 2019
• Zum Satz des Pythagoras (LA)
  Sara Tirler, Winter Term 2018/19
• Axiomatische projektive Geometrie
  Laurens Wittchow, Winter Term 2018/19 - University of Leipzig
• Eine Erweiterung der Oberschelpschen Klassenlogik samt einem einfachen Proof-Checker
  Milon Brunner, Winter Term 2018/19 - University of Leipzig
• Lineare Optimierung in der Schule mit Geogebra (LA)
  Theres Mair, Winter Term 2017/18
• Graphentheorie im Schulunterricht (LA) 
  Theresa Müssigang, Winter Term 2017/18
• In wie viele Teile teilen n Linien die Ebene? (LA)
  Barbara Pritzi, Winter Term 2017/18
• Axiomatisches Origami (LA)
  Michael Strobl, Winter Term 2017/18
• Topological Data Analysis
  Martin Berger, Winter Term 2017/18 (with Tobias Hell)
• Exakte Algorithmen zur Lösung von linearen Matrixungleichungen
  Craig Antweiler, Summer Term 2016 - University of Leipzig
• Determinantal Representations and Kirchhoff's Theorem
  Tom Drescher, Winter Term 2012/13 - University of Leipzig (with Andreas Thom)
• Matrixstellensätze
  Randolf Ihrig, Winter Term 2008/09 - University of Konstanz (with Claus Scheiderer)

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BACHELOR PROJECTS

• CHSH Inequalities
  Clemens Walder, ongoing
• Popescu-Rohrlich Boxes
  Leon Sexl, ongoing
• Channel Capacities
  Alexander Huter, ongoing
• Entanglement Witnesses in Generalized Probabilistic Theories
  Moritz Langer, ongoing
• Purification in Generalized Probabilistic Theories
  Felix Campidell, Winter Term 2025/26
• Euler's Entangled Officers
  Hannah Veit, Summer Term 2025
• Lösbarkeit und Unlösbarkeit von polynomialen Gleichungen (LA)
  Melanie West, Summer Term 2025
• Elliptische Kurven
  Jonas Völzke, Summer Term 2025
• Clifford-Algebren
  Botond Horkowicz-Kovats, Summer Term 2025
• Primärzerlegung von Idealen
  Alexander Bindhammer, Summer Term 2025
• Inclusion Index for Convex Cones
  Svenja Sturma, Winter Term 2024/25
• Zyklische Codes
  Patrick Pircher, Summer Term 2024
• Tensorrang und Matrixmultiplikation
  Emma Erharter, Summer Term 2024
• Sheaf Cohomology and Network Coding
  Nadia Fellin, Summer Term 2024
• Dimension and Degree of Ideals
  Judith Lindtner, Winter Term 2023/24
• Slack Matrices of Polytopes
  Julia Überbacher, Winter Term 2023/24
• Unendliche Galois Theory
  Anna Medwed, Winter Term 2023/24 
• Über Quaternionen-Algebren
  Valentin Ferst, Winter Term 2023/24
• Sums of Squares of Rational Polynomials 
  Elias Brenn, Winter Term 2023/24
• Die Mathematik hinter einem Navigationssystem (LA)
  Theresa Floß, Summer Term 2023
• Universal Embedding Theorems in Combinatorial Game Theory
  Michael Reitmeir, Summer Term 2023
• The Theorem of Seifert and van Kampen
  Kenneth Ehi, Summer Term 2023
• On van der Waerden's Permanent Conjecture
  Sandro Mignelli, Summer Term 2023
• Quantum State Discrimination and the Distillability Problem
  Jasmin Matti, Summer Term 2023
• Numerische Irreduzible Zerlegung
  Noah Kleinschmidt, Summer Term 2023
• Abstandsmatrizen und Abstammungsbäume (LA)
  Angelika Moser, Summer Term 2022
• Primzahlverteilung im Schulunterricht (LA)
  Roshan Kreuzer, Summer Term 2022
• Topologische Beweise des Fundamentalsatzes der Algebra
  Maximilian Illmer, Summer Term 2022
• Geometric Aspects of Sets of States (Physics)
  Stefan Kremminger, Summer Term 2022  (with Gemma De las Cuevas)
• Darstellungstheorie endlicher GruppenFlorian Willmann, Winter Term 2021/22
• Von magischen Quadraten zu magischen Würfeln
  Sabina Malik, Winter Term 2021/22
• Hilbert's 3. Problem
  Oliver Zeilerbauer, Summer Term 2021
• Der Fundamentalsatz der Algebra
  Magdalena Steuxner, Summer Term 2021
• Completely Positive Maps in Natural Language Processing
  Andreas Mair, Summer Term 2021
• Coxetergruppen
  Mathias Gschwendtner, Winter Term 2020/21
• Zur axiomatischen Methode (LA)
  Romana Würtenberger, Winter Term 2020/21
• On the Sheldon-Conjecture
  Alexander Obernauer, Winter Term 2020/21
• Der kombinatorische Nullstellensatz (LA)
  Matthias Schwab, Winter Term 2020/21
• Approximation konvexer Mengen durch Polytope
  Thomas Rottensteiner, Summer Term 2020
• Vollständig positive und kopositive Matrizen
  Sigrid Schwarzer, Summer Term 2020
• The Theorem of Nagata-Higman
  Oliver Mayr, Summer Term 2020
• Rubiks Cube als gruppentheoretisches Problem
  Josef Königsrainer, Summer Term 2020
• Matrix Completion Problems
  Hannah Entner, Summer Term 2020
• Subgroups of Free Groups
  Wolfram Gröbner, Summer Term 2019
• Das Amitsur-Levitsky Theorem
  Florian Stolz, Summer Term 2019
• Approximation von niedrigem Rang in semidefiniter Optimierung und Quadratsummen
  Hannes Lerchner, Summer Term 2019
• Operator Systems and Separability of Quantum States
  Inga Valentiner-Branth, Summer Term 2019 
• Simplification Methods for Sums of Squares Programming
  Mirco Berner, Summer Term 2018
• Random Walks on Finite Graphs and Groups
  Sarah Schneeberger, Summer Term 2018
• Finding Closest Points in Polytopes
  Carolina Carvalhido, Summer Term 2018
• Cylindrical Algebraic Decomposition for Semialgebraic Sets
  Daniel Niederlechner, Summer Term 2017
• Zum inversen Galois-Problem
  Julia Jöchler, Summer Term 2017
• Die Vermutung von Casas-Alvero
  Johanna Lercher, Summer Term 2016
• On the Positive Semidefinite Polytope Rank
  David Trieb, Summer Term 2016
• Quadratsummen von rationalen Polynomen
  Eva-Kristin Schneider, Winter Term 2014/15 - University of Leipzig
• Die Algebra des Rubik's Cube
  Tom Medak, Summer Term 2014 - University of Leipzig
• Geschichte der mathematischen Rechenhilfsmittel
  Carolin Koser, Winter Term 2013/14 - University of Leipzig 

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PAST TEACHING

• Linear Algebra
• Algebra
• Algebraic Geometry
• Real Algebraic Geometry
• Operator Algebra
• Geometry of Linear Matrix Inequalities
• Convexity
• Logic and Model Theory
• Gödel's Incompleteness Theorems
• Discrete Structures for Computer Scientists
• Basic Algebra and Number Theory for Teachers
• History and Philosophy of Mathematics