BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:John Voight (University of Sydney) DTSTART:20241031T040000Z DTEND:20241031T050000Z DTSTAMP:20260404T094318Z UID:CompAlgSemMagma/1 DESCRIPTION:Title: 17T7 is a Galois group over the rationals\nby John Voig ht (University of Sydney) as part of Computational algebra seminar\n\nLect ure held in SMRI Seminar Room - Macleay Building A12 Room 301.\n\nAbstract \nUsing Magma\, we prove that the transitive permutation group 17T7 is a G alois group over the rationals\, completing the list of transitive subgrou ps ordered by degree up to 23 (leaving the Mathieu group on 23 letters as the next missing group). \nWe exhibit such a Galois extension as the fiel d of definition of 2-torsion on an\nabelian fourfold with real multiplicat ion defined over a real quadratic field with Galois alignment. We find su ch fourfolds using Hilbert modular forms. \nFinally\, building upon work of Dembele\, we show how to (conjecturally) reconstruct the period matrix for abelian variety attached to a Hilbert modular form\; we then use this to construct an explicit degree 17 polynomial with Galois group 17T7. \nT his is joint work with Raymond van Bommel\, Edgar Costa\, Noam Elkies\, Ti mo Keller\, and Sam Schiavone.\n LOCATION:https://stable.researchseminars.org/talk/CompAlgSemMagma/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Madeleine Kyng DTSTART:20241114T040000Z DTEND:20241114T050000Z DTSTAMP:20260404T094318Z UID:CompAlgSemMagma/2 DESCRIPTION:by Madeleine Kyng as part of Computational algebra seminar\n\n Lecture held in SMRI Seminar Room - Macleay Building A12 Room 301.\nAbstra ct: TBA\n LOCATION:https://stable.researchseminars.org/talk/CompAlgSemMagma/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Lewis Combes (University of Sydney) DTSTART:20250220T040000Z DTEND:20250220T050000Z DTSTAMP:20260404T094318Z UID:CompAlgSemMagma/3 DESCRIPTION:Title: Computing mod p Selmer groups\nby Lewis Combes (Univers ity of Sydney) as part of Computational algebra seminar\n\nLecture held in SMRI Seminar Room - Macleay Building A12 Room 301.\n\nAbstract\nSelmer gr oups arise naturally in computational problems\, such as determining the r ank of an elliptic curve. p-adic Galois representations also have associat ed Selmer groups\; the Bloch-Kato conjecture says these ranks are controll ed by the order of vanishing of an L-function. While an analogue of this picture is expected to exist for mod p Galois representations\, very littl e is concretely known. We present a method to compute Selmer groups associ ated to mod p Galois representations\, using class field theory. We presen t data collected on the distribution of ranks of mod 2 Selmer groups\, as well as some interesting examples mod 3. Finally\, we speculate on appropr iate analogues of the main constructions in the Bloch-Kato conjecture in t he mod p setting.\n LOCATION:https://stable.researchseminars.org/talk/CompAlgSemMagma/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Bill Unger (University of Sydney) DTSTART:20250306T040000Z DTEND:20250306T050000Z DTSTAMP:20260404T094318Z UID:CompAlgSemMagma/4 DESCRIPTION:Title: Permutation Group Algorithms - Normal structure\nby Bil l Unger (University of Sydney) as part of Computational algebra seminar\n\ nLecture held in SMRI Seminar Room - Macleay Building A12 Room 301.\n\nAbs tract\nI will talk about Magma's suite of permutation group algorithms for computing useful\nnormal subgroups of a permutation group. In particular I will discuss the soluble radical\nmethod for group calculations and how Magma computes the normal subgroups needed to \neffectively use this. Find ing the socle of a primitive group is particularly important\, \nand our m ethods make use of the Classification of Finite Simple Groups.\n\nIn sever al cases the algorithms are unpublished improvements on published algorith ms.\n LOCATION:https://stable.researchseminars.org/talk/CompAlgSemMagma/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Stephan Elsenhans (University of Sydney) DTSTART:20250227T040000Z DTEND:20250227T050000Z DTSTAMP:20260404T094318Z UID:CompAlgSemMagma/5 DESCRIPTION:Title: Heuristic\, conditional and unconditional computation of cl ass groups and unit groups\nby Stephan Elsenhans (University of Sydney ) as part of Computational algebra seminar\n\nLecture held in SMRI Seminar Room - Macleay Building A12 Room 301.\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/CompAlgSemMagma/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Juanita Duque-Rosero (Boston) DTSTART:20250515T050000Z DTEND:20250515T060000Z DTSTAMP:20260404T094318Z UID:CompAlgSemMagma/6 DESCRIPTION:Title: An algorithm for Computing Local Heights on Hyperelliptic C urves in Quadratic Chabauty\nby Juanita Duque-Rosero (Boston) as part of Computational algebra seminar\n\nLecture held in SMRI Seminar Room - Ma cleay Building A12 Room 301.\n\nAbstract\nThe method of quadratic Chabauty is a powerful tool for\ndetermining the set of rational points on curves. A key component of\nthis method is the computation of local height functi ons. In this\ntalk\, we present an algorithm for computing these local hei ghts at odd\nprimes v not equal to p for hyperelliptic curves. Through\nap plications\, we demonstrate how this work extends the reach of\nquadratic Chabauty to curves previously considered inaccessible.\nFinally\, we provi de details on the Magma implementation of this\nalgorithm. This is joint work with Alexander Betts\, Sachi Hashimoto\,\nand Pim Spelier.\n LOCATION:https://stable.researchseminars.org/talk/CompAlgSemMagma/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Wadim Zudilin (Radboud) DTSTART:20250807T050000Z DTEND:20250807T060000Z DTSTAMP:20260404T094318Z UID:CompAlgSemMagma/7 DESCRIPTION:Title: Strange gamma evaluations\nby Wadim Zudilin (Radboud) a s part of Computational algebra seminar\n\nLecture held in SMRI Seminar Ro om - Macleay Building A12 Room 301.\n\nAbstract\nTime & Place: 3:05-4pm\, Thursday 7 August\, SMRI Seminar Rm\nAbstract:\nI will review - algorithmi cally and philosophically - strategies \nproducing closed forms for the va lues of hypergeometric functions.\n LOCATION:https://stable.researchseminars.org/talk/CompAlgSemMagma/7/ END:VEVENT BEGIN:VEVENT SUMMARY:J. Maurice Rojas (Texas A&M) DTSTART:20250821T050000Z DTEND:20250821T060000Z DTSTAMP:20260404T094318Z UID:CompAlgSemMagma/8 DESCRIPTION:Title: On Signs of Trinomials and Hypergeometric Series\nby J. Maurice Rojas (Texas A&M) as part of Computational algebra seminar\n\nLec ture held in SMRI Seminar Room - Macleay Building A12 Room 301.\n\nAbstrac t\nA curious question of Koiran is whether one can efficiently decide the signs of univariate trinomials evaluated on rational numbers. More precise ly: \n \n Given H and D\, and a polynomial\n f(x) := c_1 + c_2 x^d + c_3 x^D \n with |c_i|<=H and 0Integer multiplication is at least as hard as matrix transp osition\nby David Harvey (UNSW) as part of Computational algebra semin ar\n\nLecture held in SMRI Seminar Room - Macleay Building A12 Room 301.\n \nAbstract\nIt was recently proved that two $n$-bit integers may be\nmulti plied in $O(n \\log n)$ steps on a multitape Turing machine. This\nbound i s believed to be optimal\, but no lower bounds have been\nestablished beyo nd the trivial $\\Omega(n)$ bound. In a paper to be\npresented at FOCS 202 5 in Sydney later this year\, Joris van der Hoeven\nand I give a reduction from the \\emph{transposition problem} for binary\nmatrices to the intege r multiplication problem. There is a simple\nfolklore algorithm that trans poses an $n \\times n$ binary matrix in\ntime $O(n^2 \\log n)$. Again\, th is is believed to be optimal\, but no\nproof is known. Our new reduction i mplies that if this transposition\nalgorithm is optimal\, then integer mul tiplication satisfies the\nexpected $\\Omega(n \\log n)$ lower bound. In t his talk I will give an\noverview of how the reduction works.\n LOCATION:https://stable.researchseminars.org/talk/CompAlgSemMagma/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Florian Breuer (Newcastle) DTSTART:20250925T050000Z DTEND:20250925T060000Z DTSTAMP:20260404T094318Z UID:CompAlgSemMagma/10 DESCRIPTION:Title: Coefficients of modular polynomials\nby Florian Breuer (Newcastle) as part of Computational algebra seminar\n\nLecture held in S MRI Seminar Room - Macleay Building A12 Room 301.\n\nAbstract\nFor every p ositive integer N there is a modular polynomial $\\Phi_N(X\,Y)$ with integ er\ncoefficients which vanishes precisely at pairs $(j_1\, j_2)$ of j-inva riants of elliptic \ncurves linked by a cyclic isogeny of degree N. These polynomials play an important role \nin cryptography and algorithmic numbe r theory. \n\nI will give a student-friendly introduction to these polynom ials and review what is \nknown about the (rapid!) growth of their coeffic ients. Finally\, I will present some new \nresults showing that these coef ficients are highly divisible by small primes.\n LOCATION:https://stable.researchseminars.org/talk/CompAlgSemMagma/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Sam Frengley (Bristol) DTSTART:20251030T040000Z DTEND:20251030T050000Z DTSTAMP:20260404T094318Z UID:CompAlgSemMagma/11 DESCRIPTION:Title: Minimisation algorithms over function fields and applicati ons\nby Sam Frengley (Bristol) as part of Computational algebra semina r\n\nLecture held in SMRI Seminar Room - Macleay Building A12 Room 301.\n\ nAbstract\n"Minimisation" algorithms (and their sibling "reduction"\nalgor ithms) have proved a very fruitful tool in number theory\, dating at\nleas t to Gauss' study of integral binary quadratic forms. Since then\,\nthese algorithms have seen a remarkable variety of applications in\nnumber theor y. In computation they are regularly used to study (for\nexample) class gr oups\, descent on elliptic curves\, reduction of\nquadratic forms. On the other hand\, they also play a pivotal role in\nmany theoretical results\, notably in great advances in arithmetic\nstatistics in recent decades.\n\n I will discuss the (folklore) "geometric" versions of these algorithms\,\n exploiting the analogy between number fields and function fields (or\nspec tra of rings of integers and curves). I will illustrate their\nutility usi ng some examples arising from Hilbert modular surfaces\nleading to minimis ing conics over QQ(x\,y) (joint with Alex Cowan and\nKimball Martin) and s mall degree covers of PP^2. Time permitting\, I may\ndiscuss a more theore tical application: classifying which rational\nscrolls contain degree 5 co vers of PP^1 (a case of the Tschirnhausen\nrealisation problem) which is j oint with Sameera Vemulapalli.\n LOCATION:https://stable.researchseminars.org/talk/CompAlgSemMagma/11/ END:VEVENT BEGIN:VEVENT SUMMARY:John Voight (Sydney) DTSTART:20251009T040000Z DTEND:20251009T050000Z DTSTAMP:20260404T094318Z UID:CompAlgSemMagma/12 DESCRIPTION:Title: Ranks of elliptic curves\nby John Voight (Sydney) as p art of Computational algebra seminar\n\nLecture held in SMRI Seminar Room - Macleay Building A12 Room 301.\n\nAbstract\nSpeaker: John Voight (Sydney )\nTitle: Ranks of elliptic curves\nTime & Place: 15.00-16.00\, Thursday 9 October\, SMRI Seminar Room\nAbstract:\nElliptic curves lie at the inters ection of many areas of mathematics and remain \ncentral to modern number theory. The rank of an elliptic curve over the rational \nnumbers measures the size of its group of rational points\; intuitively\, it counts \nthe number of independent points needed to generate all rational solutions up to \ntorsion. A fundamental question\, going back to Poincaré\, remains unresolved: can \nthe rank be arbitrarily large? \nIn this talk\, we pres ent computations and data\, a statistical model and heuristic \nframework to guide our expectations\, and outliers that challenge these assumptions. \nThis is joint work with Jennifer Park\, Bjorn Poonen\, and Melanie Matc hett Wood.\n LOCATION:https://stable.researchseminars.org/talk/CompAlgSemMagma/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Reymond Akpanya (Sydney) DTSTART:20251113T040000Z DTEND:20251113T050000Z DTSTAMP:20260404T094318Z UID:CompAlgSemMagma/13 DESCRIPTION:Title: On the Construction of Edge-transitive Surfaces\nby R eymond Akpanya (Sydney) as part of Computational algebra seminar\n\nLectur e held in SMRI Seminar Room - Macleay Building A12 Room 301.\n\nAbstract\n A simplicial surface can be seen as the incidence geometry of the vertices \, edges and faces of a triangulated 2-manifold. We call such a surface ed ge-transitive\, if its automorphism group acts transitively on the edges o f the surface. A given simplicial surface can be linked to a cubic graph b y recording the incidences between the corresponding faces and edges. The resulting cubic graph does not directly contain any information on the ver tices of the corresponding surface. This missing information is obtained b y constructing a cycle double cover of the corresponding cubic graph\, i.e . a collection of cycles such that every edge of the graph lies in exactly two cycles.\n\nIn this talk\, we discuss the construction of edge-transit ive surfaces by providing suitable cycle double covers of edge-transitive cubic graphs. We show that there exist four types of edge-transitive surfa ces\, splitting up further into a total of five sub-types. We exploit our theoretical results to compute a census of edge-transitive surfaces with up to 5000 faces.\n LOCATION:https://stable.researchseminars.org/talk/CompAlgSemMagma/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Edgar Costa (MIT) DTSTART:20251127T040000Z DTEND:20251127T050000Z DTSTAMP:20260404T094318Z UID:CompAlgSemMagma/14 DESCRIPTION:Title: Computing isogeny classes of genus 2 Jacobians over Q\ nby Edgar Costa (MIT) as part of Computational algebra seminar\n\nLecture held in SMRI Seminar Room - Macleay Building A12 Room 301.\n\nAbstract\nGi ven a genus 2 curve C over Q\, its Jacobian J(C) is a 2-dimensional analog ue \nof an elliptic curve. Just as for elliptic curves\, one can look at t he isogeny \nclass of J(C): all abelian surfaces over Q that are linked to J(C) by an isogeny.\n\nIn this talk I will describe a practical algorithm which\, starting from a genus \n2 curve C/Q whose Jacobian has trivial ge ometric endomorphism ring\, computes all \ngenus 2 curves D/Q whose Jacobi ans are isogenous to J(C) over Q. I will outline the \nmain ideas behind t he method\, which use information from Galois representations \nattached t o J(C) together with a mix of analytic and algebraic tools to prove or \nr ule out the existence of isogenies\, and I will illustrate the algorithm w ith \nnumerical examples.\n\nThis is joint work with Raymond van Bommel\, Shiva Chidambaram\, and Jean Kieffer.\n LOCATION:https://stable.researchseminars.org/talk/CompAlgSemMagma/14/ END:VEVENT BEGIN:VEVENT SUMMARY:Kamilla Rekvenyi (Manchester) DTSTART:20260219T040000Z DTEND:20260219T050000Z DTSTAMP:20260404T094318Z UID:CompAlgSemMagma/15 DESCRIPTION:Title: An algebraic generalisation of a graph theory problem\ nby Kamilla Rekvenyi (Manchester) as part of Computational algebra seminar \n\nLecture held in SMRI Seminar Room.\n\nAbstract\nIn this talk\, I will introduce a new permutation-group invariant inspired by a classical proble m in graph theory. Specifically\, for a transitive permutation group G act ing on a set Ω\, we define the parameter sep(G)\, which denotes the size of the smallest set of points A⊆Ω such that\, for every permutation g i n G\, the intersection of A with its image A^g is nonempty. I will present recent results concerning this parameter.\n\nThis is joint work with Marc o Barbieri\, Maruša Lekše\, and Primož Potočnik.\n LOCATION:https://stable.researchseminars.org/talk/CompAlgSemMagma/15/ END:VEVENT BEGIN:VEVENT SUMMARY:Bettina Eick (Braunschweig) DTSTART:20260226T040000Z DTEND:20260226T050000Z DTSTAMP:20260404T094318Z UID:CompAlgSemMagma/16 DESCRIPTION:Title: A survey of algorithms for polycyclic groups\nby Betti na Eick (Braunschweig) as part of Computational algebra seminar\n\nLecture held in SMRI Seminar Room - Macleay Building A12 Room 301.\n\nAbstract\nW hat do polycyclic groups look like and how can one compute with such \ngro ups? The basics of this have been known for a long time and this \ntalk re calls them briefly. It then describes various special types of\npolycyclic groups and some of their algorithmic methods: finite soluble \ngroups\, f initely generated nilpotent groups\, polycyclic crystallographic \ngroups\ , polycyclic groups arising from algebraic number fields are interesting\n examples. The talk also highlights some recent advances in this area and\n mentions some open problems.\n LOCATION:https://stable.researchseminars.org/talk/CompAlgSemMagma/16/ END:VEVENT BEGIN:VEVENT SUMMARY:Michael Monagan (Simon Fraser) DTSTART:20260305T040000Z DTEND:20260305T050000Z DTSTAMP:20260404T094318Z UID:CompAlgSemMagma/17 DESCRIPTION:Title: Efficiency Problems in the History of Maple\nby Michae l Monagan (Simon Fraser) as part of Computational algebra seminar\n\nLectu re held in SMRI Seminar Room - Macleay Building A12 Room 301.\n\nAbstract\ nThe first paper on Maple was published and presented in 1983. The paper \ nwas entitled "The Design of Maple: a compact\, portable and powerful\nCom puter Algebra System". Powerful meant that Maple could solve a wide\nrang e of problems in a reasonable time. However\, the early versions\nof Mapl e were not efficient. One reason for this was that the main\ncompetition\ , Reduce and Macsyma\, were also not very efficient. I will\npresent six efficiency problems that were identified\, how they were fixed\,\nand some lessons I learned about designing and implementing a Computer\nAlgebra Sy stem. I'll also compare Maple with Magma and show that Magma is\nvery slo w on some problems. I'll end with a status update on polynomial\nfactoriz ation implementations and show some timing benchmarks comparing\nMaple\, M agma\, Singular and Maxima.\n LOCATION:https://stable.researchseminars.org/talk/CompAlgSemMagma/17/ END:VEVENT BEGIN:VEVENT SUMMARY:Michael Monagan (Simon Fraser) DTSTART:20260312T040000Z DTEND:20260312T050000Z DTSTAMP:20260404T094318Z UID:CompAlgSemMagma/18 DESCRIPTION:Title: Factoring Multivariate Polynomials given by Black Boxes\nby Michael Monagan (Simon Fraser) as part of Computational algebra semi nar\n\nLecture held in SMRI Seminar Room - Macleay Building A12 Room 301.\ n\nAbstract\nThe black box model for computing with polynomials was introd uced\nto Computer Algebra by Kaltofen and Trager in 1990. Kaltofen's PhD\ nstudent Angel Diaz subsequently implemented GCD and factorization\nalgori thms for polynomials represented by a black box in C++. Little work\nhas been done since and no Computer Algebra Systems are using the black\nbox m odel.\n\nIn the last 5 years we have designed and implemented a black box\ nalgorithm for factoring a polynomial given by a black box. We have used\ nit to compute the factors of determinants of matrices of polynomials.\n\n In the talk I will present the black box model for a polynomial\nf in n va riables x1\,x2\,...xn over a field F. I will explain why it is\nmore powe rful than the standard sparse representation for polynomials\, and\nhow we can compute with it. Then I'll present our black box polynomial\nfactori zation algorithm with some timing benchmarks to show how good\nit is.\n\nT his is joint work with my former PhD student Tian Chen.\n LOCATION:https://stable.researchseminars.org/talk/CompAlgSemMagma/18/ END:VEVENT BEGIN:VEVENT SUMMARY:Adam Logan (Waterloo) DTSTART:20260402T040000Z DTEND:20260402T050000Z DTSTAMP:20260404T094318Z UID:CompAlgSemMagma/19 DESCRIPTION:Title: The Kodaira dimension of Hilbert modular threefolds\nb y Adam Logan (Waterloo) as part of Computational algebra seminar\n\nLectur e held in SMRI Seminar Room - Macleay Building A12 Room 301.\n\nAbstract\n Following a method introduced by Thomas-Vasquez and developed by Grundman\ , we prove that many Hilbert modular threefolds of geometric genus 0 and 1 are of general type\, and that some are of nonnegative Kodaira dimension. The new ingredient is a detailed study of the geometry and combinatorics of totally positive integral elements of a fractional ideal in a totally r eal number field that are minimal with respect to trace up to multiplicati on by totally positive units.\n LOCATION:https://stable.researchseminars.org/talk/CompAlgSemMagma/19/ END:VEVENT BEGIN:VEVENT SUMMARY:Raymond van Bommel (Bristol) DTSTART:20260430T050000Z DTEND:20260430T060000Z DTSTAMP:20260404T094318Z UID:CompAlgSemMagma/20 DESCRIPTION:by Raymond van Bommel (Bristol) as part of Computational algeb ra seminar\n\nLecture held in SMRI Seminar Room - Macleay Building A12 Roo m 301.\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/CompAlgSemMagma/20/ END:VEVENT BEGIN:VEVENT SUMMARY:Rhys Evans (Sydney) DTSTART:20260326T040000Z DTEND:20260326T050000Z DTSTAMP:20260404T094318Z UID:CompAlgSemMagma/21 DESCRIPTION:Title: Orderly generation of generating sets\nby Rhys Evans ( Sydney) as part of Computational algebra seminar\n\nLecture held in SMRI S eminar Room - Macleay Building A12 Room 301.\n\nAbstract\nIn general\, the enumeration of discrete objects is computationally hard. However\, for ma ny highly symmetrical discrete objects\, their description as a finite gro up together with a generating set with certain properties often allows for more efficient computation and deeper theory (e.g.\, regular maps\, manip lexes and Cayley graphs).\n      \nIn this talk\, we will see the application of an orderly generation algorithm to the enumeration of m inimal generating sets of a given group. Simple group-theoretical observat ions will be used to improve on a basic algorithm\, extending previous enu merations to groups of much larger order. This has been used to generate a complete list of minimal Cayley graphs on up to 511 vertices. I will also mention other collections of highly symmetrical discrete objects\, and th e databases and packages that make the resulting collections of objects av ailable to a wider audience.\n\nThis is based on joint work with Primož P otočnik and Kolja Knauer.\n LOCATION:https://stable.researchseminars.org/talk/CompAlgSemMagma/21/ END:VEVENT BEGIN:VEVENT SUMMARY:Jack J. Garzella (UCSD) DTSTART:20260423T050000Z DTEND:20260423T060000Z DTSTAMP:20260404T094318Z UID:CompAlgSemMagma/23 DESCRIPTION:Title: Zeta functions on projective hypersurfaces via controlled reduction\nby Jack J. Garzella (UCSD) as part of Computational algebra seminar\n\nLecture held in SMRI Seminar Room - Macleay Building A12 Room 301.\n\nAbstract\nThe zeta function of a variety in characteristic p captu res a lot of arithmetic information about that variety. Calculating this z eta function as fast as possible is a classical problem in computational n umber theory. We describe a cohomological approach called *controlled redu ction*\, due to Costa and Harvey\, which is the state of the art for many varieties of dimension greater than one. We describe various ways one can improve the algorithms of Costa and Harvey\, including an "abstract contro lled reduction problem" which abstracts the algorithm away from the specif ics of any particular class of varieties. Using our algorithms\, we find m any examples of varieties with interesting arithmetic invariants (like New ton polygons and domino numbers). All work is joint with Batubara\, Huang\ , and Mellberg.\n LOCATION:https://stable.researchseminars.org/talk/CompAlgSemMagma/23/ END:VEVENT END:VCALENDAR