Průniky algebry, geometrie a informatiky

Intersections of algebra, geometry, and informatics

Projekt univerzitních výzkumných center UNCE/24/SCI/022 (interní číslo: 301–44/204087)

Cílem projektu je podporovat mladé vědce pracující v oblastech, v nichž se prolínají algebra, geometrie a informatika. Projekt trvá v období 1. 1. 2024 – 31. 12. 2029 na Matematicko-fyzikální fakultě Univerzity Karlovy.

Senioři:

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

Postdoci:

• Isaac Bird
• Nikola Jedličková
• Jan Kotrbatý
• Jun Maillard
• Akash Singha Roy
• Robin Visser
• Jordan Williamson
• Patrick Wynne

Studenti:

• Antonio Del Donno
• Daria Pavlova
• Maroš Grego
• Dominik Krasula
• Gabriel Krejčí
• Phoebe MacDougall
• Michal Molnár
• Adam Morawski
• Kateřina Panešová
• Martina Petráková
• Martin Romaňák
• Yagmur Sak
• Filip Šťastný
• Tomáš Vítek

Bývalí účastníci na projektu:

• Dominick Beck
• Souvik Dey (postdoc)
• Frederik Ďalak
• Ondřej Ježil
• Iva Karafiátová
• Aaron Kettner
• Erik Kočandrle
• Michael Kompatscher (postdoc)
• Aibat Kossumov
• Mykyta Narusevych
• Jindřich Novák
• Dayoon Park (postdoc)
• Om Prakash
• Bryant Rosado Silva
• Bernardo Rossi (postdoc)
• Chiara Sava
• Filippo Spaggiari
• Pavlo Yatsyna (postdoc)
• Yifan Zhang
• Martin Zika

Manažerka grantu:

• Martina Vaváčková

Publikace:

• A. Kettner. Cuntz–Pimsner algebras of partial automorphisms twisted by vector bundles II: Nuclear dimension. https://arxiv.org/html/2506.16630v1
• M.Barrero, T. Barthel, L. Pol, N. Strickland, and J. Williamson. The spectrum of global representations for families of bounded rank and VI-modules. https://arxiv.org/abs/2506.21525
• N. Daans, S. Gajović, S. H. Man, P. Yatsyna. Pythagoras numbers for infinite algebraic fields. https://arxiv.org/abs/2502.11222
• M. Tinková, P. Yatsyna. Non-decomposable quadratic forms over totally real number fields. https://arxiv.org/abs/2502.05991
• M. Tinková, R. Visser, P. Yatsyna. Sums of two units in number fields. https://arxiv.org/abs/2502.01345
• V. Kala, J. Krásenský, D. Park, P. Yatsyna, B. Żmija. Kitaoka's conjecture for quadratic fields. https://arxiv.org/abs/2501.19371
• A. Bhaduri, S. Dey, P. Lank. Preservation for generation along the structure morphism of coherent algebras over a scheme. https://londmathsoc.onlinelibrary.wiley.com/doi/10.1112/blms.70066
• M. Barriero, T. Barthel, L. Pol, N. Strickland, and J. Williamson. Global representation theory: Homological foundations. https://arxiv.org/abs/2505.21449
• J. Kotrbatý. On a generalization of Godbersen's conjecture. https://arxiv.org/abs/2502.02149
• I. Bird, J. Williamson, A. Zvonareva. The shift-homological spectrum and parametrising kernels of rank functions. https://arxiv.org/abs/2502.11939
• D. Beck, Z. Lv, A. Potechin. On the second moment of the determinant of random symmetric, Wigner, and Hermitian matrices. https://arxiv.org/abs/2409.14620
• D. Beck.On Random Simplex Picking Beyond the Blashke Problem.https://arxiv.org/abs/2412.07952
• S. Balchin, J.P.C. Greenlees, L. Pol, J. Williamson. Torsion models for tensor-triangulated categories. https://arxiv.org/abs/2501.05180
• 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
• M. Kompatscher, P. Mayr. Every finite nilpotent loop has a supernilpotent loop as reduct. https://arxiv.org/abs/2409.12484
• 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.