Department of Mathematics and Computer Science

Casper Asbjørn Eriksen defends his PhD thesis at a public lecture: “Computational Methods for Molecular Structures: Biochemical Data Integration and Enumeration”.Professor Kim Skak Larsen will act as chairman at the defence.The PhD defence takes place in IMADA Conference Room (Ø18-509-2).All are welcome.

Esben Andreas Wrona Bay Sørensen defends his PhD thesis at a public lecture: “Data Science and Visualization Concerns in Interdisciplinary Research of Changes in the Arctic Ocean”.Associate Professor Tariq Yousef will act as chairman at the defence.The PhD defence takes place in U140 (Ø16-501-1).All are welcome.

Students develop a wide range of competences throughout their education, but they do not always recognise everything they become better at along the way.

Joël Beimler defends his PhD thesis at a public lecture: “Mirror Symmetry for the Painlevé Character Varieties”.Associate Professor Fabian Haiden will act as chairman at the defence.The PhD defence takes place in U31 (V5-601-1).All are welcome.

Camilla Vang Østergaard defends his PhD thesis at a public lecture: “Methodological and Practical Considerations of Visual Digital Storytelling for the Heritage of Nazi Persecution”.Associate Professor Tariq Yousef will act as chairman at the defence.The PhD defence takes place in U140 (Ø16-501-1).All are welcome.

Nicolai Dinh Khang Truong defends his PhD thesis at a public lecture: “Machine Learning for Rare Disease Diagnosis: Data Quality, Generalizability and Interoperability”.Associate Professor Veit Schwämmle will act as chairman at the defence.The PhD defence takes place in U170 (Ø21-600c-1).All are welcome.

Speaker: Sebastian Pögel (​University of Zurich).Abstract: TBA

Speaker: Apoorv Tiwari (​University of Southern Denmark).Abstract: Fault-tolerant quantum computation can incur a substantial resource cost when a desired logical operation must be constructed from a restricted set of logical primitives. To make such operations directly available, I will introduce irrep surface codes (ISCs), two-dimensional topological quantum error-correcting codes engineered to transversally implement a prescribed set of logical gates. The target logical gates only need to satisfy two conditions: (i) they generate a finite group, which, up to global phases, is forced by the Eastin-Knill theorem, and (ii) they are irreducible, meaning that any operator commuting with the set of gates must be proportional to the identity. This accommodates arbitrary finite groups of diagonal gates and arbitrary reversible classical gates, since each can be embedded into a larger irreducible finite group of gates. It also enables logical gates outside every finite level of the Clifford hierarchy. To incorporate these operations into surface-code computations, we further develop lattice-surgery protocols to transfer the encoded information between surface codes and ISCs obeying one of two sufficient conditions. Together, these results establish a systematic method for tailoring topological codes to desired logical operations and integrating them into conventional computations.

Rasmus Jensen defends his PhD thesis at a public lecture: “Geometric Interpolation on the Stiefel and Grassmann Manifolds”.Associate Professor Benjamin Jäger will act as chairman at the defence.The PhD defence takes place in U31 (V5-601-1).All are welcome.

Speaker: Jury Ivan Radkovski (​University of Copenhagen).Abstract: A tropical quantum field theory is an exactly solvable deformation limit of an ordinary QFT, governed by a non-linear partial differential equation. We use the integrable two-dimensional sine-Gordon theory as a testbench to compare the exact features of an undeformed model with its tropical counterpart. We classify scale-invariant tropical QFTs in D = 2 and leverage functional renormalization group methods to demonstrate that all scale-invariant theories with periodic effective actions are infrared fixed points of flows originating from sine-Gordon Lagrangians. For the tropical sine-Gordon model, we compute the β-functions exactly, solve the renormalized theory both via a convergent expansion and numerically for all admissible couplings, and illustrate the complete renormalization group flow from the Gaussian to the IR fixed point. Finally, we study the large-order behaviour of the loop expansion and relate it to the Hamilton-Jacobi equation, whose solutions we interpret as tropical instantons.

Speaker: Arim Song (​Friedrich-Alexander University Erlagen-Nürnberg).Abstract: $W$-algebras are families of vertex algebras associated with Lie algebras and their nilpotent elements. They can be viewed as chiral analogues of the Feigin-Frenkel center of the Lie algebra and exhibit rich structures, including Feigin–Frenkel duality and coset realizations. The $W_\infty$-algebra is a two-parameter family of vertex algebras whose quotients recover type A principal $W$-algebras. It provides a powerful framework for classifying vertex algebras with prescribed strong generating type and has led to the discovery of isomorphisms among various families of vertex algebras, including results that partially establish the celebrated triality conjecture of Gaiotto and Rapčák. The construction of $W$-algebras extends naturally to Lie superalgebras, giving rise to $W$-superalgebras. However, many questions concerning dualities among these algebras remain open. In recent joint work with Creutzig, Kovalchuk, Linshaw, and Suh, we extended the $W_\infty$-algebra framework to type A Lie superalgebras and established dualities for type A principal $W$-superalgebras. In this talk, I will introduce $W$-algebras and $W_\infty$-algebras, and discuss their structural properties. If time permits, I will briefly discuss the recent developments in the super setting.