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Entries for this week: 7

Monday February 03, 2025

Mathematics Colloquium [url]
Quantum Codes From Symmetry
- Eric Kubischta, University of Maryland
Time: 3:05 Room: 101
Abstract/Desc: Quantum computers are inherently subject to noise, necessitating fault-tolerant quantum error-correcting codes to achieve quantum advantage. This requires performing logical operations indirectly, through physical operations that preserve the codespace. While generic physical operations are not fault-tolerant, transversal gates, which act locally on individual qubits, are intrinsically fault-tolerant, making them particularly appealing for practical implementation. The set of logical operations achievable with transversal gates forms a finite group G that is an invariant of equivalent quantum codes. In this talk, I will present my recent contributions to a novel top-down approach to quantum error correction, where quantum codes are systematically derived from the group G. Using tools from the representation theory of finite and unitary groups, I will show how the structure of G informs the construction of quantum codes and governs their error-correcting properties. This perspective not only reveals novel quantum codes but also highlights deep connections between representation theory and the foundations of quantum error correction.

Tuesday February 04, 2025

Special Biomathematics Seminar
N-Body Oscillator Interactions of Higher-Order Coupling Functions
- Youngmin Park, University of Florida
Time: 11:35 Room: 301 Love
Abstract/Desc: We introduce a method to identify phase equations that include N-body interactions for general coupled oscillators, valid beyond the weak coupling approximation. This strategy is an extension of the theory from [Y. Park and D. Wilson, SIAM J. Appl. Dyn. Syst., 20 (2021), pp. 1464--1484] and yields coupling functions for N general limit-cycle oscillators with arbitrary types of coupling, in a similar spirit to the classic theory of weakly coupled oscillators. These coupling functions enable the study of oscillator networks in terms of phase-locked states, whose stability can be determined using straightforward linear stability arguments. We demonstrate the utility of this approach by reducing and analyzing N = 3 conductance-based thalamic neuron models: the reduction correctly predicts a loss in stability of a splay state for nonweak synaptic coupling. We conclude with a brief remark on recent extensions to n:m phase-locking with heterogeneous oscillators.

Geometry and Topology Seminar [url]
A family of diffeomorphisms on real rational surfaces
- Kyounghee Kim, FSU
Time: 3:05 Room: 232
More Information
Abstract/Desc: We will explore the dynamics of a family of real diffeomorphisms derived from complex rational surface automorphisms

ACM seminar
Optimal control for Darcy’s flow in a heterogeneous porous media
- SeongHee Jeong, FSU
Time: 3:05 pm Room: 0231
Abstract/Desc: In this work, we investigate optimal control problems in heterogeneous porous media. Based on the partial differential equation constraint connecting the state and the control, we produce the associated control as a dependent quantity of the state. Then, we introduce the reduced optimal control problem which contains only the state variable. Here we employ $C^0$ interior penalty finite element methods for the spatial discretization to solve the reduced optimal control problem resulting in a fourth-order variational inequality. We provide a priori error estimates and stability analyses. Several numerical examples validate and illustrate the capabilities of the proposed algorithm.

Thursday February 06, 2025

Financial Mathematics Seminar
- Ali kara, FSU
Time: 3:05 Room: LOV 0231

Algebra seminar
Even periodization
- Rok Gregoric, John Hopkins University
Time: 3:05PM Room: 232
Abstract/Desc: In this talk, I will present work in progress on even periodization. This is an operation on spectral stacks, which roughly approximates them as closely as possible with affines corresponding to even periodic ring spectra. This turns out to have close connections to the even filtration of Hahn-Raksit-Wilson, the prismatization stacks of Bhatt-Lurie, as well as the chromatic affineness results for topological modular forms of Mathew-Meier.

Friday February 07, 2025

Data Science and Machine Learning Seminar
A survey of tight spans
- Mario Gomez, FSU
Time: 1:20 Room: Lov 106
Abstract/Desc: Given a metric space (X, d), its tight span T(X,d) is a universal metric space that contains an isometric copy of X. Thanks in part to its universal properties, tight spans have many desirable properties, like being a contractible geodesic space. In a 2024 paper (whose preprint was published in 2020), Lim, Mémoli and Okutan found a link between topological data analysis and tight spans. More precisely, they proved that the Vietoris-Rips complex of X is homotopy equivalent to a union of balls around X inside of its tight span. In this talk, I will give a survey of the properties of the tight span, including the aforementioned theorem and some applications to topological data analysis.

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Department of Mathematics

This Week in Mathematics