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:20260422T212604Z UID:CompAlgSemMagma/1 DESCRIPTION:Title: 17T7 is a Galois group over the rationals\nby John Voight (Uni versity of Sydney) as part of Computational algebra seminar\n\nLecture hel d in SMRI Seminar Room - Macleay Building A12 Room 301.\n\nAbstract\nUsing Magma\, we prove that the transitive permutation group 17T7 is a Galois g roup over the rationals\, completing the list of transitive subgroups orde red by degree up to 23 (leaving the Mathieu group on 23 letters as the nex t missing group). \nWe exhibit such a Galois extension as the field of de finition of 2-torsion on an\nabelian fourfold with real multiplication def ined over a real quadratic field with Galois alignment. We find such four folds using Hilbert modular forms. \nFinally\, building upon work of Demb ele\, we show how to (conjecturally) reconstruct the period matrix for abe lian variety attached to a Hilbert modular form\; we then use this to cons truct an explicit degree 17 polynomial with Galois group 17T7. \nThis is joint work with Raymond van Bommel\, Edgar Costa\, Noam Elkies\, Timo Kell er\, and Sam Schiavone.\n LOCATION:https://researchseminars.org/talk/CompAlgSemMagma/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Madeleine Kyng DTSTART:20241114T040000Z DTEND:20241114T050000Z DTSTAMP:20260422T212604Z 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://researchseminars.org/talk/CompAlgSemMagma/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Lewis Combes (University of Sydney) DTSTART:20250220T040000Z DTEND:20250220T050000Z DTSTAMP:20260422T212604Z UID:CompAlgSemMagma/3 DESCRIPTION:Title: Computing mod p Selmer groups\nby Lewis Combes (University of Sydney) as part of Computational algebra seminar\n\nLecture held in SMRI S eminar Room - Macleay Building A12 Room 301.\n\nAbstract\nSelmer groups ar ise naturally in computational problems\, such as determining the rank of an elliptic curve. p-adic Galois representations also have associated Selm er groups\; the Bloch-Kato conjecture says these ranks are controlled by t he order of vanishing of an L-function. While an analogue of this picture is expected to exist for mod p Galois representations\, very little is co ncretely known. We present a method to compute Selmer groups associated to mod p Galois representations\, using class field theory. We present data collected on the distribution of ranks of mod 2 Selmer groups\, as well as some interesting examples mod 3. Finally\, we speculate on appropriate an alogues of the main constructions in the Bloch-Kato conjecture in the mod p setting.\n LOCATION:https://researchseminars.org/talk/CompAlgSemMagma/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Bill Unger (University of Sydney) DTSTART:20250306T040000Z DTEND:20250306T050000Z DTSTAMP:20260422T212604Z UID:CompAlgSemMagma/4 DESCRIPTION:Title: Permutation Group Algorithms - Normal structure\nby Bill Unger (University of Sydney) as part of Computational algebra seminar\n\nLectur e held in SMRI Seminar Room - Macleay Building A12 Room 301.\n\nAbstract\n I will talk about Magma's suite of permutation group algorithms for comput ing useful\nnormal subgroups of a permutation group. In particular I will discuss the soluble radical\nmethod for group calculations and how Magma c omputes the normal subgroups needed to \neffectively use this. Finding the socle of a primitive group is particularly important\, \nand our methods make use of the Classification of Finite Simple Groups.\n\nIn several case s the algorithms are unpublished improvements on published algorithms.\n LOCATION:https://researchseminars.org/talk/CompAlgSemMagma/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Stephan Elsenhans (University of Sydney) DTSTART:20250227T040000Z DTEND:20250227T050000Z DTSTAMP:20260422T212604Z UID:CompAlgSemMagma/5 DESCRIPTION:Title: Heuristic\, conditional and unconditional computation of class gro ups and unit groups\nby Stephan Elsenhans (University of Sydney) as pa rt of Computational algebra seminar\n\nLecture held in SMRI Seminar Room - Macleay Building A12 Room 301.\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/CompAlgSemMagma/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Juanita Duque-Rosero (Boston) DTSTART:20250515T050000Z DTEND:20250515T060000Z DTSTAMP:20260422T212604Z UID:CompAlgSemMagma/6 DESCRIPTION:Title: An algorithm for Computing Local Heights on Hyperelliptic Curves i n Quadratic Chabauty\nby Juanita Duque-Rosero (Boston) as part of Comp utational algebra seminar\n\nLecture held in SMRI Seminar Room - Macleay B uilding A12 Room 301.\n\nAbstract\nThe method of quadratic Chabauty is a p owerful tool for\ndetermining the set of rational points on curves. A key component of\nthis method is the computation of local height functions. In this\ntalk\, we present an algorithm for computing these local heights at odd\nprimes v not equal to p for hyperelliptic curves. Through\napplicati ons\, we demonstrate how this work extends the reach of\nquadratic Chabaut y to curves previously considered inaccessible.\nFinally\, we provide deta ils on the Magma implementation of this\nalgorithm. This is joint work wi th Alexander Betts\, Sachi Hashimoto\,\nand Pim Spelier.\n LOCATION:https://researchseminars.org/talk/CompAlgSemMagma/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Wadim Zudilin (Radboud) DTSTART:20250807T050000Z DTEND:20250807T060000Z DTSTAMP:20260422T212604Z UID:CompAlgSemMagma/7 DESCRIPTION:Title: Strange gamma evaluations\nby Wadim Zudilin (Radboud) as part of Computational algebra seminar\n\nLecture held in SMRI Seminar Room - Ma cleay Building A12 Room 301.\n\nAbstract\nTime & Place: 3:05-4pm\, Thursda y 7 August\, SMRI Seminar Rm\nAbstract:\nI will review - algorithmically a nd philosophically - strategies \nproducing closed forms for the values of hypergeometric functions.\n LOCATION:https://researchseminars.org/talk/CompAlgSemMagma/7/ END:VEVENT BEGIN:VEVENT SUMMARY:J. Maurice Rojas (Texas A&M) DTSTART:20250821T050000Z DTEND:20250821T060000Z DTSTAMP:20260422T212604Z UID:CompAlgSemMagma/8 DESCRIPTION:Title: On Signs of Trinomials and Hypergeometric Series\nby J. Mauric e Rojas (Texas A&M) as part of Computational algebra seminar\n\nLecture he ld in SMRI Seminar Room - Macleay Building A12 Room 301.\n\nAbstract\nA cu rious question of Koiran is whether one can efficiently decide the signs o f univariate trinomials evaluated on rational numbers. More precisely: \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 transposition \nby David Harvey (UNSW) as part of Computational algebra seminar\n\nL ecture held in SMRI Seminar Room - Macleay Building A12 Room 301.\n\nAbstr act\nIt was recently proved that two $n$-bit integers may be\nmultiplied i n $O(n \\log n)$ steps on a multitape Turing machine. This\nbound is belie ved to be optimal\, but no lower bounds have been\nestablished beyond the trivial $\\Omega(n)$ bound. In a paper to be\npresented at FOCS 2025 in Sy dney later this year\, Joris van der Hoeven\nand I give a reduction from t he \\emph{transposition problem} for binary\nmatrices to the integer multi plication problem. There is a simple\nfolklore algorithm that transposes a n $n \\times n$ binary matrix in\ntime $O(n^2 \\log n)$. Again\, this is b elieved to be optimal\, but no\nproof is known. Our new reduction implies that if this transposition\nalgorithm is optimal\, then integer multiplica tion satisfies the\nexpected $\\Omega(n \\log n)$ lower bound. In this tal k I will give an\noverview of how the reduction works.\n LOCATION:https://researchseminars.org/talk/CompAlgSemMagma/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Florian Breuer (Newcastle) DTSTART:20250925T050000Z DTEND:20250925T060000Z DTSTAMP:20260422T212604Z UID:CompAlgSemMagma/10 DESCRIPTION:Title: Coefficients of modular polynomials\nby Florian Breuer (Newca stle) as part of Computational algebra seminar\n\nLecture held in SMRI Sem inar Room - Macleay Building A12 Room 301.\n\nAbstract\nFor every positive integer N there is a modular polynomial $\\Phi_N(X\,Y)$ with integer\ncoe fficients which vanishes precisely at pairs $(j_1\, j_2)$ of j-invariants of elliptic \ncurves linked by a cyclic isogeny of degree N. These polynom ials play an important role \nin cryptography and algorithmic number theor y. \n\nI will give a student-friendly introduction to these polynomials an d review what is \nknown about the (rapid!) growth of their coefficients. Finally\, I will present some new \nresults showing that these coefficient s are highly divisible by small primes.\n LOCATION:https://researchseminars.org/talk/CompAlgSemMagma/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Sam Frengley (Bristol) DTSTART:20251030T040000Z DTEND:20251030T050000Z DTSTAMP:20260422T212604Z UID:CompAlgSemMagma/11 DESCRIPTION:Title: Minimisation algorithms over function fields and applications \nby Sam Frengley (Bristol) as part of Computational algebra seminar\n\nLe cture held in SMRI Seminar Room - Macleay Building A12 Room 301.\n\nAbstra ct\n"Minimisation" algorithms (and their sibling "reduction"\nalgorithms) have proved a very fruitful tool in number theory\, dating at\nleast to Ga uss' study of integral binary quadratic forms. Since then\,\nthese algorit hms have seen a remarkable variety of applications in\nnumber theory. In c omputation they are regularly used to study (for\nexample) class groups\, descent on elliptic curves\, reduction of\nquadratic forms. On the other h and\, they also play a pivotal role in\nmany theoretical results\, notably in great advances in arithmetic\nstatistics in recent decades.\n\nI will discuss the (folklore) "geometric" versions of these algorithms\,\nexploit ing the analogy between number fields and function fields (or\nspectra of rings of integers and curves). I will illustrate their\nutility using some examples arising from Hilbert modular surfaces\nleading to minimising con ics over QQ(x\,y) (joint with Alex Cowan and\nKimball Martin) and small de gree covers of PP^2. Time permitting\, I may\ndiscuss a more theoretical a pplication: classifying which rational\nscrolls contain degree 5 covers of PP^1 (a case of the Tschirnhausen\nrealisation problem) which is joint wi th Sameera Vemulapalli.\n LOCATION:https://researchseminars.org/talk/CompAlgSemMagma/11/ END:VEVENT BEGIN:VEVENT SUMMARY:John Voight (Sydney) DTSTART:20251009T040000Z DTEND:20251009T050000Z DTSTAMP:20260422T212604Z UID:CompAlgSemMagma/12 DESCRIPTION:Title: Ranks of elliptic curves\nby John Voight (Sydney) as part of Computational algebra seminar\n\nLecture held in SMRI Seminar Room - Macle ay Building A12 Room 301.\n\nAbstract\nSpeaker: John Voight (Sydney)\nTitl e: Ranks of elliptic curves\nTime & Place: 15.00-16.00\, Thursday 9 Octobe r\, SMRI Seminar Room\nAbstract:\nElliptic curves lie at the intersection of many areas of mathematics and remain \ncentral to modern number theory. The rank of an elliptic curve over the rational \nnumbers measures the si ze of its group of rational points\; intuitively\, it counts \nthe number of independent points needed to generate all rational solutions up to \nto rsion. A fundamental question\, going back to Poincaré\, remains unreso lved: can \nthe rank be arbitrarily large? \nIn this talk\, we present com putations and data\, a statistical model and heuristic \nframework to guid e our expectations\, and outliers that challenge these assumptions. \nThis is joint work with Jennifer Park\, Bjorn Poonen\, and Melanie Matchett Wo od.\n LOCATION:https://researchseminars.org/talk/CompAlgSemMagma/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Reymond Akpanya (Sydney) DTSTART:20251113T040000Z DTEND:20251113T050000Z DTSTAMP:20260422T212604Z UID:CompAlgSemMagma/13 DESCRIPTION:Title: On the Construction of Edge-transitive Surfaces\nby Reymond Akpanya (Sydney) as part of Computational algebra seminar\n\nLecture held in SMRI Seminar Room - Macleay Building A12 Room 301.\n\nAbstract\nA simpl icial surface can be seen as the incidence geometry of the vertices\, edge s and faces of a triangulated 2-manifold. We call such a surface edge-tran sitive\, if its automorphism group acts transitively on the edges of the s urface. A given simplicial surface can be linked to a cubic graph by recor ding the incidences between the corresponding faces and edges. The resulti ng cubic graph does not directly contain any information on the vertices o f the corresponding surface. This missing information is obtained by const ructing a cycle double cover of the corresponding cubic graph\, i.e. a col lection of cycles such that every edge of the graph lies in exactly two cy cles.\n\nIn this talk\, we discuss the construction of edge-transitive sur faces by providing suitable cycle double covers of edge-transitive cubic g raphs. We show that there exist four types of edge-transitive surfaces\, s plitting up further into a total of five sub-types. We exploit our theore tical results to compute a census of edge-transitive surfaces with up to 5 000 faces.\n LOCATION:https://researchseminars.org/talk/CompAlgSemMagma/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Edgar Costa (MIT) DTSTART:20251127T040000Z DTEND:20251127T050000Z DTSTAMP:20260422T212604Z UID:CompAlgSemMagma/14 DESCRIPTION:Title: Computing isogeny classes of genus 2 Jacobians over Q\nby Edg ar Costa (MIT) as part of Computational algebra seminar\n\nLecture held in SMRI Seminar Room - Macleay Building A12 Room 301.\n\nAbstract\nGiven a g enus 2 curve C over Q\, its Jacobian J(C) is a 2-dimensional analogue \nof an elliptic curve. Just as for elliptic curves\, one can look at the isog eny \nclass of J(C): all abelian surfaces over Q that are linked to J(C) b y 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 geometric endomorphism ring\, computes all \ngenus 2 curves D/Q whose Jacobians are isogenous to J(C) over Q. I will outline the \nmain ideas behind the meth od\, which use information from Galois representations \nattached to J(C) together with a mix of analytic and algebraic tools to prove or \nrule out the existence of isogenies\, and I will illustrate the algorithm with \nn umerical examples.\n\nThis is joint work with Raymond van Bommel\, Shiva C hidambaram\, and Jean Kieffer.\n LOCATION:https://researchseminars.org/talk/CompAlgSemMagma/14/ END:VEVENT BEGIN:VEVENT SUMMARY:Kamilla Rekvenyi (Manchester) DTSTART:20260219T040000Z DTEND:20260219T050000Z DTSTAMP:20260422T212604Z UID:CompAlgSemMagma/15 DESCRIPTION:Title: An algebraic generalisation of a graph theory problem\nby Kam illa Rekvenyi (Manchester) as part of Computational algebra seminar\n\nLec ture held in SMRI Seminar Room.\n\nAbstract\nIn this talk\, I will introdu ce a new permutation-group invariant inspired by a classical problem in gr aph theory. Specifically\, for a transitive permutation group G acting 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 in G\, t he intersection of A with its image A^g is nonempty. I will present recent results concerning this parameter.\n\nThis is joint work with Marco Barbi eri\, Maruša Lekše\, and Primož Potočnik.\n LOCATION:https://researchseminars.org/talk/CompAlgSemMagma/15/ END:VEVENT BEGIN:VEVENT SUMMARY:Bettina Eick (Braunschweig) DTSTART:20260226T040000Z DTEND:20260226T050000Z DTSTAMP:20260422T212604Z UID:CompAlgSemMagma/16 DESCRIPTION:Title: A survey of algorithms for polycyclic groups\nby Bettina Eick (Braunschweig) as part of Computational algebra seminar\n\nLecture held i n SMRI Seminar Room - Macleay Building A12 Room 301.\n\nAbstract\nWhat do polycyclic groups look like and how can one compute with such \ngroups? Th e basics of this have been known for a long time and this \ntalk recalls t hem briefly. It then describes various special types of\npolycyclic groups and some of their algorithmic methods: finite soluble \ngroups\, finitely generated nilpotent groups\, polycyclic crystallographic \ngroups\, polyc yclic groups arising from algebraic number fields are interesting\nexample s. The talk also highlights some recent advances in this area and\nmention s some open problems.\n LOCATION:https://researchseminars.org/talk/CompAlgSemMagma/16/ END:VEVENT BEGIN:VEVENT SUMMARY:Michael Monagan (Simon Fraser) DTSTART:20260305T040000Z DTEND:20260305T050000Z DTSTAMP:20260422T212604Z UID:CompAlgSemMagma/17 DESCRIPTION:Title: Efficiency Problems in the History of Maple\nby Michael Monag an (Simon Fraser) as part of Computational algebra seminar\n\nLecture held in SMRI Seminar Room - Macleay Building A12 Room 301.\n\nAbstract\nThe fi rst paper on Maple was published and presented in 1983. The paper \nwas en titled "The Design of Maple: a compact\, portable and powerful\nComputer A lgebra System". Powerful meant that Maple could solve a wide\nrange of pr oblems in a reasonable time. However\, the early versions\nof Maple were not efficient. One reason for this was that the main\ncompetition\, Reduc e and Macsyma\, were also not very efficient. I will\npresent six efficie ncy problems that were identified\, how they were fixed\,\nand some lesson s I learned about designing and implementing a Computer\nAlgebra System. I'll also compare Maple with Magma and show that Magma is\nvery slow on so me problems. I'll end with a status update on polynomial\nfactorization i mplementations and show some timing benchmarks comparing\nMaple\, Magma\, Singular and Maxima.\n LOCATION:https://researchseminars.org/talk/CompAlgSemMagma/17/ END:VEVENT BEGIN:VEVENT SUMMARY:Michael Monagan (Simon Fraser) DTSTART:20260312T040000Z DTEND:20260312T050000Z DTSTAMP:20260422T212604Z UID:CompAlgSemMagma/18 DESCRIPTION:Title: Factoring Multivariate Polynomials given by Black Boxes\nby M ichael Monagan (Simon Fraser) as part of Computational algebra seminar\n\n Lecture held in SMRI Seminar Room - Macleay Building A12 Room 301.\n\nAbst ract\nThe black box model for computing with polynomials was introduced\nt o Computer Algebra by Kaltofen and Trager in 1990. Kaltofen's PhD\nstuden t Angel Diaz subsequently implemented GCD and factorization\nalgorithms fo r polynomials represented by a black box in C++. Little work\nhas been do ne since and no Computer Algebra Systems are using the black\nbox model.\n \nIn the last 5 years we have designed and implemented a black box\nalgori thm for factoring a polynomial given by a black box. We have used\nit to compute the factors of determinants of matrices of polynomials.\n\nIn the talk I will present the black box model for a polynomial\nf in n variables x1\,x2\,...xn over a field F. I will explain why it is\nmore powerful th an the standard sparse representation for polynomials\, and\nhow we can co mpute with it. Then I'll present our black box polynomial\nfactorization algorithm with some timing benchmarks to show how good\nit is.\n\nThis is joint work with my former PhD student Tian Chen.\n LOCATION:https://researchseminars.org/talk/CompAlgSemMagma/18/ END:VEVENT BEGIN:VEVENT SUMMARY:Adam Logan (Waterloo) DTSTART:20260402T040000Z DTEND:20260402T050000Z DTSTAMP:20260422T212604Z UID:CompAlgSemMagma/19 DESCRIPTION:Title: The Kodaira dimension of Hilbert modular threefolds\nby Adam Logan (Waterloo) as part of Computational algebra seminar\n\nLecture held in SMRI Seminar Room - Macleay Building A12 Room 301.\n\nAbstract\nFollowi ng a method introduced by Thomas-Vasquez and developed by Grundman\, we pr ove that many Hilbert modular threefolds of geometric genus 0 and 1 are of general type\, and that some are of nonnegative Kodaira dimension. The ne w ingredient is a detailed study of the geometry and combinatorics of tota lly positive integral elements of a fractional ideal in a totally real num ber field that are minimal with respect to trace up to multiplication by t otally positive units.\n LOCATION:https://researchseminars.org/talk/CompAlgSemMagma/19/ END:VEVENT BEGIN:VEVENT SUMMARY:Raymond van Bommel (Bristol) DTSTART:20260430T050000Z DTEND:20260430T060000Z DTSTAMP:20260422T212604Z 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://researchseminars.org/talk/CompAlgSemMagma/20/ END:VEVENT BEGIN:VEVENT SUMMARY:Rhys Evans (Sydney) DTSTART:20260326T040000Z DTEND:20260326T050000Z DTSTAMP:20260422T212604Z 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 Seminar Room - Macleay Building A12 Room 301.\n\nAbstract\nIn general\, the enumer ation of discrete objects is computationally hard. However\, for many high ly symmetrical discrete objects\, their description as a finite group toge ther with a generating set with certain properties often allows for more e fficient computation and deeper theory (e.g.\, regular maps\, maniplexes a nd Cayley graphs).\n      \nIn this talk\, we will see the app lication of an orderly generation algorithm to the enumeration of minimal generating sets of a given group. Simple group-theoretical observations wi ll be used to improve on a basic algorithm\, extending previous enumeratio ns to groups of much larger order. This has been used to generate a comple te list of minimal Cayley graphs on up to 511 vertices. I will also mentio n other collections of highly symmetrical discrete objects\, and the datab ases and packages that make the resulting collections of objects available to a wider audience.\n\nThis is based on joint work with Primož Potočni k and Kolja Knauer.\n LOCATION:https://researchseminars.org/talk/CompAlgSemMagma/21/ END:VEVENT BEGIN:VEVENT SUMMARY:Jack J. Garzella (UCSD) DTSTART:20260423T050000Z DTEND:20260423T060000Z DTSTAMP:20260422T212604Z UID:CompAlgSemMagma/23 DESCRIPTION:Title: Modular Design in p-adic point counting algorithms\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\nWe wil l give an intro\, from a programmer's point of view\, to point counting al gorithms via p-adic cohomology. We describe common problems with the major ity (or perhaps all) of the existing implementations. Then\, we will descr ibe a new implementation\, found in the DeRham.jl library\, meant to addre ss some of these issues.\n LOCATION:https://researchseminars.org/talk/CompAlgSemMagma/23/ END:VEVENT BEGIN:VEVENT SUMMARY:Stephen Glasby (UWA) DTSTART:20260521T050000Z DTEND:20260521T060000Z DTSTAMP:20260422T212604Z UID:CompAlgSemMagma/24 DESCRIPTION:Title: The probability that two elements with large 1-eigenspaces genera te a classical group\nby Stephen Glasby (UWA) as part of Computational algebra seminar\n\nLecture held in SMRI Seminar Room - Macleay Building A 12 Room 301.\n\nAbstract\nThere has been much research\, by many different authors\, on matrix group algorithms. Given a finitely generated subgroup G of a finite general linear group GL(d\,q)\, the first step is to find a composition series for G\, this involves finding the simple groups from w hich G is "built". After chopping G into indivisible parts\, one has to "r ecognize" the simple groups. The most common (non-cyclic) simple groups to recognize are the classical groups\, and the core case involves recognizi ng classical groups acting on their natural module. Existing algorithms c onstruct a naturally embedded classical subgroup H of G which is generated by new generators g1\, g2 which have large 1-eigenspaces. We prove that w e can find g1\, g2 withhigh probability\, and that g1\, g2 generate H with probability at least 0.97.\n\nThis result appears in an 80 page preprint with Alice Niemeyer (Aachen) and Cheryl Praeger (UWA)\, and took us about 6 years to complete. I will give an overview of the working parts of this project.\n LOCATION:https://researchseminars.org/talk/CompAlgSemMagma/24/ END:VEVENT BEGIN:VEVENT SUMMARY:Andrew Mathas (Sydney) DTSTART:20260514T050000Z DTEND:20260514T060000Z DTSTAMP:20260422T212604Z UID:CompAlgSemMagma/25 DESCRIPTION:Title: Computing decomposition numbers of symmetric groups\nby Andre w Mathas (Sydney) as part of Computational algebra seminar\n\nLecture held in SMRI Seminar Room - Macleay Building A12 Room 301.\n\nAbstract\nI will describe an algorithm for computing decomposition numbers of the symmetri c groups over finite fields. The approach is based on Young's seminormal f orm from the semisimple representation theory of the symmetric groups\, bu t cast in very different clothes from the non-semisimple representation th eory of cyclotomic KLR algebras. These algebras include the group algebras of the symmetric groups as a special case. Computationally\, the advantag es are that we can use the speed of the semisimple representation theory c ombined with idempotent truncation to compute Gram matrices on significant ly spaces than are accessible using classical approaches. The resulting co de works for cyclotomic KLR algebras of affine type A or C of arbitrary do minant weight. If time permits\, I will discuss a large family of very exp licit and "relatively small" counterexamples to the James conjecture that were found this way.\n LOCATION:https://researchseminars.org/talk/CompAlgSemMagma/25/ END:VEVENT END:VCALENDAR