Universität Wien

250044 SE Algebra (2025S)

4.00 ECTS (2.00 SWS), SPL 25 - Mathematik
Continuous assessment of course work

Registration/Deregistration

Note: The time of your registration within the registration period has no effect on the allocation of places (no first come, first served).

Details

max. 25 participants
Language: English

Lecturers

Classes (iCal) - next class is marked with N

During the first meeting on Monday 03.03. we will give a brief introduction to the three topics chosen for the seminar and schedule the presentations.

  • Monday 03.03. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 10.03. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 17.03. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 24.03. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 31.03. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 07.04. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 28.04. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 05.05. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 12.05. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 19.05. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 26.05. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 02.06. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 16.06. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 23.06. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 30.06. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock

Information

Aims, contents and method of the course

This is a student seminar focusing on 3 different topics in Algebra/Number theory. Each of them will be presented in 3 or 4 lectures, to be prepared and held by the students, and building on each other. The topics in this semester are the following:

Topic 1. (J. Mahnkopf)
TBA

Topic 2. (A. Mínguez)
Sarnak's Letter on Quantum Gates and Arithmetic

This topic for the reading seminar explores Peter Sarnak’s manuscript letter on quantum gates (https://publications.ias.edu/sites/default/files/Letter%20-%20golden%20gates%20march_0.pdf), where he examines the arithmetic foundations of efficient universal quantum gates. Classical circuits rely on Boolean functions f:{0,1}^n→{0,1}, built from logic gates like AND, OR, and NOT, with complexity measured by circuit length. In contrast, quantum computing replaces bits with qubits—unit vectors in C^2 —and logic gates with 2×2 unitary matrices that preserve quantum state norms. Sarnak's idea is to construct optimal gate sets by approximating elements of G=PSU(2) with minimal height, drawing connections between quantum computation and the arithmetic of quaternion algebras. He highlights the role of number theory and automorphic forms in designing efficient quantum gates, offering insights into improving quantum circuit design. Prior knowledge of algebraic number theory is recommended.

Topic 3. (H. Grobner)
Modular forms à la Siegel

Assessment and permitted materials

Regular participation to the presentations and presentation of a topic.

Minimum requirements and assessment criteria

Regular participation at the talks and presentation of a topic.

Examination topics

Reading list

Will be assigned individually for each topic.

Association in the course directory

MALS

Last modified: Sa 01.03.2025 00:02