Intersections of algebra, geometry, and informatics

Průniky algebry, geometrie a informatiky

Charles University Research Center program No. UNCE/24/SCI/022 (internal: 301–44/204087)

The aim of the project is to support junior scientists working in the intersections of algebra, geometry, and informatics. The project starts 1 Jan 2024 and ends 31 Dec 2029, at Faculty of Mathematics and Physics, Charles University

Seniors:

• Libor Barto (PI)
• Jan Krajíček
• Jan Rataj
• Jan Šťovíček

Postdocs:

• Stanislav Nagy
• Jan Kotrbatý
• Isaac Bird
• Jordan Williamson
• Souvik Dey
• Jun Maillard
• Michael Kompatscher
• Pavlo Yatsyna
• Dayoon Park

Students:

• Ondřej Ježil
• Mykyta Narusevych
• Yifan Zhang
• Phoebe MacDougall
• Yagmur Sak
• Chiara Sava
• Filippo Spaggiari
• Om Prakash
• Bryant Rosado Silva
• Frederik Ďalak
• Aaron Kettner
• Martin Zika
• Dominick Beck
• Iva Karafiátová
• Martina Petráková

Former participants on the project:

• Bernardo Rossi (senior)

Grant Manager:

• Johanka Čablíková

Publications:

• A. Del Donno, E. Latini, T. Weber. On the Durdevic approach to quantum principal bundles. https://arxiv.org/abs/2404.07944
• E. Ken, M. Narusevych. Ajtai's theorem for T22® and pebble games with backtracking. https://arxiv.org/abs/2406.10924
• O. Ježil. Limits of structures and Total NP Search Problems. https://arxiv.org/abs/2301.13603
• N. Daans, V. Kala, S. H. Man, M. Widmer, P. Yatsyna. Most totally real fields do not have universal forms or Northcott property. https://arxiv.org/abs/2409.11082
• O. Chwiedziuk, M. Doležálek, S. Hlavinková, E. Pěchoučková, Z. Pezlar, O. Prakash, A. Růžičková, M. Zindulka. No proper generalized quadratic forms are universal over quadratic fields. https://arxiv.org/abs/2409.07941
• N. Daans, V. Kala, J. Krásenský, P. Yatsyna. Failures of integral Springer's theorem. https://arxiv.org/abs/2404.12844
• O. Chwiedziuk, M. Doležálek, E. Pěchoučková, Z. Pezlar, O. Prakash, G. Romeo, A. Růžičková, M. Zindulka. Representing rational integers by generalized quadratic forms over quadratic fields https://arxiv.org/abs/2403.07171
• V. Kala, P. Yatsyna. Even better sums of squares over quintic and cyclotomic fields. https://arxiv.org/abs/2402.03850
• O. Prakash. Northcott property and universality of higher degree forms. Int. J. Number Theory (to appear). https://doi.org/10.48550/arXiv.2407.19974
• G. Cherubini, P. Yatsyna. There are Salem numbers with trace −3 and every degree at least 34. Exp. Math. To appear. https://doi.org/10.1080/10586458.2024.2337223

• V. Kala, O. Prakash (2024). There is no 290-Theorem for higher degree forms. Math. Nachr. (to appear). https://arxiv.org/abs/2405.10660
• Aaron Kettner (2024). Cuntz–Pimsner algebras of partial automorphisms twisted by vector bundles I: Fixed point algebra, simplicity and the tracial state space. https://doi.org/10.48550/arXiv.2408.10047
• Filip Bočinec, Stanislav Nagy (2024). Conditions for equality in Anderson’s theorem, Statistics & Probability Letters. https://doi.org/10.1016/j.spl.2024.110094

• Xiaohui Liu, Yuzi Liu, Petra Laketa, Stanislav Nagy, Yuting Chen (2024). Exact and approximate computation of the scatter halfspace depth. Computational Statistics, To appear. doi.org/10.1007/s00180–024–01500–6

• Stanislav Nagy, Petra Laketa (2024). Theoretical properties of angular halfspace depth. Bernoulli, To appear.