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:

Postdoci:

Studenti:

  • Břetislav Andr
  • Antonio Del Donno
  • Ondřej Chwiedziuk
  • Giovanni Gava
  • Maryia Kapytka
  • Dominik Krasula
  • Phoebe MacDougall
  • Michal Molnár
  • Kateřina Panešová
  • Martina Petráková
  • Martin Romaňák
  • Yagmur Sak
  • Filip Šťastný

Bývalí účastníci na projektu:

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

Manažerka grantu:

Publikace:

  • 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
  • D. Beck, On random simplex picking beyond the Blashke problem, Methodol. Comput. Appl. Probab. 28 (2026), article 53, 45 pp., DOI
  • M. Barriero, T. Barthel, L. Pol, N. Strickland, J. Williamson, Global representation theory: Homological foundations, Tunis. J. Math. 8 (3) (2026), 539–578, DOI
  • S. Haag, P. Samanta, Swati, H. Swisher, S. Treneer, R. Visser, Repellent properties of perfect powers on partition functions: a heuristic approach, Res. Math. Sci. 13 (2026), article 40, 34 pp., DOI
  • M. K. Brown, S. Dey, G. Li, M. Sayrafi, Computing global Ext for complexes, J. Pure Appl. Algebra 230 (11) (2026), article 108365, 11 pp., DOI
  • S. Dey, P. Lank, Dévissage for generation in derived categories, Proc. Amer. Math. Soc. 154 (2026), 997–1006, 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, J. 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
  • A. Kettner, Cuntz–Pimsner algebras of partial automorphisms twisted by vector bundles I: Fixed point algebra, simplicity and the tracial state space, Münster J. Math. 18 (1) (2025), 141–180, DOI
  • S. Dey, P. Lank, Closedness of the singular locus and generation for derived categories, J. Algebra 684 (2025), 64–77, DOI
  • O. Celikbas, S. Dey, T. Kobayashi, H. Matsui, A. Sadeghi, Two theorems on the vanishing of Ext, Proc. Amer. Math. Soc. 153 (2025), 3209–3225, 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
  • S. Dey, S. Kumashiro, P. Sarkar, On a generalized Auslander-Reiten conjecture, Algebras Represent. Theory 27 (2024), 1581–1602, 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
  • 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
  • A. Bernig, J. Kotrbatý, T. Wannerer, Hard Lefschetz theorem and Hodge-Riemann relations for convex valuations, Ann. of 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
  • 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. 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
  • A. Kettner, Twisted topological graphs and Cartan subalgebras, arXiv
  • D. Krasula, Free and projective LCD codes, arXiv
  • P. Wynne, Structure and complexity of 2-nilpotent Mal'cev algebras, arXiv
  • I. Bird, Definable functors and Brown-Adams representability, arXiv
  • R. Visser, V. Ziegler, On integers that are representable as the sum of two units, arXiv
  • A. Bernig, D. Faifman, J. Kotrbatý, Invariant valuations on Lie groups, arXiv
  • A. Bernig, D. Faifman, J. Kotrbatý, The volume of tubes in Lie groups, arXiv
  • J. Kotrbatý, M. A. Mouamine, Godbersen's conjecture and the Lp-Rogers-Shephard inequality, arXiv
  • F. Fryš, J. Kotrbatý, Around higher-order Godbersen conjectures, arXiv
  • M. Schulte, M. Švarc Petráková, Point process convergence of large inradii of Poisson-Laguerre tessellations, arXiv
  • F. Genovese, C. Sava, J. Šťovíček, The derivator of a dg-category, arXiv
  • J. Maillard, J. Šťovíček, Torsion and complete dualizable objects in tensor-triangulated categories over a Noetherian ring, arXiv
  • M. Asgharzadeh, M. DeBellevue, S. Dey, S. Nasseh, R. Takahashi, Vector space summands of lower syzygies, arXiv
  • S. Dey, When are syzygies of the residue field self-dual?, arXiv
  • S. Dey, D. Ghosh, S. Pramanik, T. J. Puthenpurakal, S. Sahoo, Coherent functors, powers of ideals, and asymptotic stability, arXiv
  • S. Dey, R. Holanda, C. B. Miranda-Neto, Homological dimensions, the Gorenstein property, and special cases of some conjectures, arXiv
  • M. Grego, T. Vítek, T. Willwacher, The homology of Out(F8) and Aut(F7), arXiv