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:

Postdocs:

Students:

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

Former participants on the project:

  • 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
  • Daria Pavlova
  • Adam Morawski

Grant Manager:

Publications:

  • A. Kettner, Cuntz–Pimsner algebras of partial automorphisms twisted by vector bundles II: Nuclear dimension, J. Funct. Anal. 292 (2027), 111639, 38 pp., DOI
  • M. Tinková, R. Visser, P. Yatsyna, Sums of two units in number fields, Math. Z. 312 (2026), article 39, 21 pp., DOI
  • O. Ježil, Limits of structures and total NP search problems, Z. Math. Logik Grundlagen Math. 72 (2026), 135–156, DOI
  • 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, Ramanujan J. 69 (4) (2026), article 92, 10 pp., DOI
  • 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, New York J. Math. 32 (2026) 691–718, DOI
  • M. Kompatscher, P. Mayr, Every finite nilpotent loop has a supernilpotent loop as reduct, Results Math. 81 (2026), article 21, 16 pp., DOI
  • F. V. Fomin, P. A. Golovach, N. Jedličková, J. Kratochvíl, D. Sagunov, K. Simonov, Path cover, hamiltonicity, and independence number: An FPT perspective, STOC '26 – Proceedings of the 58th Annual ACM SIGACT Symposium on Theory of Computing (2026), 276–285, DOI
  • N. Jedličková, J. Kratochvíl, On the structure of hamiltonian graphs with small independence number, J. Comput. System Sci. 157 (2026), article 103754, 20 pp., DOI
  • J. Bok, A. Das, A. Gujgiczer, N. Jedličková, Generalizing Brook's theorem via partial coloring is hard classically and locally, Lecture Notes in Comput. Sci. 16444 (2026), 247–262, DOI
  • I. Bird, J. Williamson, Definable functoriality of tensor-triangular spectra, Pacific J. Math. 342 (1) (2026), 33–44, DOI
  • M. Tinková, P. Yatsyna, Additively indecomposable quadratic forms over totally real number fields, J. Lond. Math. Soc. 112 (5) (2025), article e70350, 23 pp., DOI
  • A. Bhaduri, S. Dey, P. Lank, Preservation for generation along the structure morphism of coherent algebras over a scheme, Bull. Lond. Math. Soc. 57 (2025), 1885–1896, DOI
  • J. Kotrbatý, On a generalization of Godbersen's conjecture, Int. Math. Res. Not. IMRN 2025 (22) (2025), 1–11, DOI
  • I. Bird, J. Williamson, A. Zvonareva, The shift-homological spectrum and parametrising kernels of rank functions, Bull. Lond. Math. Soc. 112 (6) (2025), article e70337, 58 pp., DOI
  • N. Daans, V. Kala, S. H. Man, M. Widmer, P. Yatsyna, Most totally real fields do not have universal forms or Northcott property, Proc. Natl. Acad. Sci. USA 122 (20) (2025), article e2419414122, 8 pp., DOI
  • N. Daans, V. Kala, J. Krásenský, P. Yatsyna, Failures of integral Springer's theorem, Proc. Amer. Math. Soc. 153 (6) (2025), 2369–2379, DOI
  • O. Prakash, Northcott property and universality of higher degree forms, Int. J. Number Theory 21 (3) (2025), 675–694, DOI
  • G. Cherubini, P. Yatsyna, There are Salem numbers with trace −3 and every degree at least 34, Exp. Math. 34 (2) (2025), 141–146, DOI
  • X. Liu, Y. Liu, P. Laketa, S. Nagy, Y. Chen, Exact and approximate computation of the scatter halfspace depth, Comput. Statist. 40 (2025), 547–572, DOI
  • S. Nagy, P. Laketa, Theoretical properties of angular halfspace depth, Bernoulli 31 (2) (2025), 1007–1031, DOI
  • J. Kerner, P. Yatsyna, On the spectral gap of a discrete Schrödinger operator on the path graph in the limit of large volume, Complex Anal. Oper. Theory 19 (5) (2025), article 115, 14 pp., DOI
  • J. Bok, J. Fiala, N. Jedličková, J. Kratochvíl, Computational complexity of covering regular trees, LIPIcs. Leibniz Int. Proc. Inform. 345 (2025), 26:1–26:19, DOI
  • V. Kala, O. Prakash, There is no 290-Theorem for higher degree forms, Math. Nachr. 297 (11) (2024), 4322–4332, DOI
  • F. Bočinec, S. Nagy, Conditions for equality in Anderson’s theorem, Statist. Probab. Lett. 209 (2024), article 110094, 8 pp., DOI
  • N. Daans, S. Gajović, S. H. Man, P. Yatsyna, Pythagoras numbers for infinite algebraic fields, Rev. Mat. Complut. (to appear), DOI
  • V. Kala, P. Yatsyna, Even better sums of squares over quintic and cyclotomic fields, Rev. Mat. Complut. (to appear), DOI
  • K. Gajdzica, R. Visser, M. Zakarczemny, Rectangle partitions generalizing integer partitions, Ann. Comb. (to appear), DOI
  • M. Barriero, T. Barthel, L. Pol, N. Strickland, J. Williamson, Global representation theory: Homological foundations, Tunis. J. Math. (to appear), arXiv
  • V. Kala, P. Yatsyna, B. Żmija, Real quadratic fields with a universal form of given rank have density zero, Amer. J. Math. (to appear), arXiv
  • M.Barrero, T. Barthel, L. Pol, N. Strickland, J. Williamson, The spectrum of global representations for families of bounded rank and VI-modules, arXiv
  • V. Kala, J. Krásenský, D. Park, P. Yatsyna, B. Żmija, Kitaoka's conjecture for quadratic fields, arXiv
  • D. Beck, Z. Lv, A. Potechin, On the second moment of the determinant of random symmetric, Wigner, and Hermitian matrices, arXiv
  • D. Beck, On random simplex picking beyond the Blashke problem, arXiv
  • S. Balchin, J.P.C. Greenlees, L. Pol, J. Williamson, Torsion models for tensor-triangulated categories, arXiv
  • A. Del Donno, E. Latini, T. Weber, On the Durdevic approach to quantum principal bundles, arXiv
  • E. Ken, M. Narusevych, Ajtai's theorem for T2_2® and pebble games with backtracking, arXiv
  • A. Kettner, Cuntz–Pimsner algebras of partial automorphisms twisted by vector bundles I: Fixed point algebra, simplicity and the tracial state space, arXiv
  • D. Park, R. Visser, P. Yatsyna, J. Yoon, Asymptotics of n-universal lattices over number fields, arXiv
  • P. Yatsyna, B. Żmija, Counting polynomials with positive roots, arXiv
  • D. Park, Almost regularity of m-gonal form
  • D. Park, p-order of binary quadratic form representations
  • D. Park, Proof of Friedlands conjecture from 1989: How similar are the genus mates?
  • T. Attema, M. Klooß, R. W. F. Lai, P. Yatsyna, Adaptive special soundness: Improved knowledge extraction by adaptive useful challenge sampling, arXiv
  • T. Peirce, J. Williamson, Duality in tensor-triangular geometry via proxy-smallness, arXiv
  • D. Pavlova, Boardman-Vogt tensor product and wreath product of operadic categories, arXiv
  • Z. Pawlas, M. Švarc Petráková, Mixing properties of random Laguerre tessellations, arXiv