BEGIN:VCALENDAR METHOD:PUBLISH PRODID:Microsoft Exchange Server 2010 VERSION:2.0 X-WR-CALNAME:Pure Lunchtime Seminar BEGIN:VTIMEZONE TZID:GMT Standard Time BEGIN:STANDARD DTSTART:16010101T020000 TZOFFSETFROM:+0100 TZOFFSETTO:+0000 RRULE:FREQ=YEARLY;INTERVAL=1;BYDAY=-1SU;BYMONTH=10 END:STANDARD BEGIN:DAYLIGHT DTSTART:16010101T010000 TZOFFSETFROM:+0000 TZOFFSETTO:+0100 RRULE:FREQ=YEARLY;INTERVAL=1;BYDAY=-1SU;BYMONTH=3 END:DAYLIGHT END:VTIMEZONE BEGIN:VEVENT DESCRIPTION:I will discuss the question of whether there can be an algorith m to decide contractibility of (usually finite) simplicial complexes\, whe re there are many known results and some famous open problems.\n UID:040000008200E00074C5B7101A82E00800000000ADCC1EA7A620DC01000000000000000 010000000225C5BE27E1B334F8529F94D7E952EC2 SUMMARY:Ian Leary: Deciding contractibility DTSTART;TZID=GMT Standard Time:20251013T120000 DTEND;TZID=GMT Standard Time:20251013T130000 CLASS:PUBLIC PRIORITY:5 DTSTAMP:20260810T024051Z TRANSP:OPAQUE STATUS:CONFIRMED SEQUENCE:0 LOCATION:B54 Room 10037 (10B) X-MICROSOFT-CDO-APPT-SEQUENCE:0 X-MICROSOFT-CDO-BUSYSTATUS:BUSY X-MICROSOFT-CDO-INTENDEDSTATUS:BUSY X-MICROSOFT-CDO-ALLDAYEVENT:FALSE X-MICROSOFT-CDO-IMPORTANCE:1 X-MICROSOFT-CDO-INSTTYPE:0 X-MICROSOFT-DONOTFORWARDMEETING:FALSE X-MICROSOFT-DISALLOW-COUNTER:FALSE X-MICROSOFT-REQUESTEDATTENDANCEMODE:DEFAULT X-MICROSOFT-ISRESPONSEREQUESTED:FALSE END:VEVENT BEGIN:VEVENT DESCRIPTION:When the characteristic of a field k divides the order of a fin ite group G\, representation theory becomes more subtle. In this modular s etting\, Maschke's theorem fails\, and not all kG-modules are semi-simple or even projective. The Green correspondence offers a powerful tool: under certain conditions\, it gives a bijection between the non-projective inde composable modules of G and those of a subgroup. In this talk\, we'll expl ore how this correspondence plays out in a concrete case: the group SL_2(F _p) over an algebraic closure of F_p. We'll discuss what the Green corresp ondence tells us\, the challenges in making it explicit\, and what this re veals about modular representation theory in practice.\n UID:040000008200E00074C5B7101A82E00800000000CD4330A86B2DDC01000000000000000 010000000E6F3F5D4FE0CFA4EBDD5D919E747EB9E SUMMARY:Denver-James Marchment: The p-modular Green correspondence of SL_2( F_p) DTSTART;TZID=GMT Standard Time:20251027T120000 DTEND;TZID=GMT Standard Time:20251027T130000 CLASS:PUBLIC PRIORITY:5 DTSTAMP:20260810T024051Z TRANSP:OPAQUE STATUS:CONFIRMED SEQUENCE:0 LOCATION:B54 Room 10037 (10B) X-MICROSOFT-CDO-APPT-SEQUENCE:0 X-MICROSOFT-CDO-BUSYSTATUS:BUSY X-MICROSOFT-CDO-INTENDEDSTATUS:BUSY X-MICROSOFT-CDO-ALLDAYEVENT:FALSE X-MICROSOFT-CDO-IMPORTANCE:1 X-MICROSOFT-CDO-INSTTYPE:0 X-MICROSOFT-DONOTFORWARDMEETING:FALSE X-MICROSOFT-DISALLOW-COUNTER:FALSE X-MICROSOFT-REQUESTEDATTENDANCEMODE:DEFAULT X-MICROSOFT-ISRESPONSEREQUESTED:FALSE END:VEVENT BEGIN:VEVENT DESCRIPTION:The classical Alexander trick implies that the space of homeomo rphisms of a d-dimensional disk is contractible. Recent work of Galatius –Randal-Williams and Krannich–Kupers extends this result to contractib le manifolds of dimension at least 5. We aim to give a survey of the class ical approach to studying automorphisms of manifolds in a modern language\ , and outline why these techniques currently fail to establish an analogou s result in dimension 4. If time permits\, we may briefly discuss the appr oach chosen by the authors named above\, and discuss the obstacles to exte nding it to dimension 4.\n UID:040000008200E00074C5B7101A82E0080000000021E000186C2DDC01000000000000000 010000000EB27AE62BEB05F48A42C95D26FC84B44 SUMMARY:Maximilian Hans: Automorphisms of manifolds DTSTART;TZID=GMT Standard Time:20251110T120000 DTEND;TZID=GMT Standard Time:20251110T130000 CLASS:PUBLIC PRIORITY:5 DTSTAMP:20260810T024051Z TRANSP:OPAQUE STATUS:CONFIRMED SEQUENCE:0 LOCATION:B54 Room 10037 (10B) X-MICROSOFT-CDO-APPT-SEQUENCE:0 X-MICROSOFT-CDO-BUSYSTATUS:BUSY X-MICROSOFT-CDO-INTENDEDSTATUS:BUSY X-MICROSOFT-CDO-ALLDAYEVENT:FALSE X-MICROSOFT-CDO-IMPORTANCE:1 X-MICROSOFT-CDO-INSTTYPE:0 X-MICROSOFT-DONOTFORWARDMEETING:FALSE X-MICROSOFT-DISALLOW-COUNTER:FALSE X-MICROSOFT-REQUESTEDATTENDANCEMODE:DEFAULT X-MICROSOFT-ISRESPONSEREQUESTED:FALSE END:VEVENT BEGIN:VEVENT DESCRIPTION:I will define roughly median spaces\, they include hyperbolic s paces\, trees and products of those. I will discuss group actions on rough ly median spaces and the conjecture that proper actions on Lp spaces shoul d be equivalent to proper actions on roughly median spaces.\n UID:040000008200E00074C5B7101A82E00800000000FB2808526C2DDC01000000000000000 010000000517D0C3711C79C4EB1B33848485E135A SUMMARY:Indira Chatterji (University of Côte d'Azur): Roughly median geome try DTSTART;TZID=GMT Standard Time:20251124T120000 DTEND;TZID=GMT Standard Time:20251124T130000 CLASS:PUBLIC PRIORITY:5 DTSTAMP:20260810T024051Z TRANSP:OPAQUE STATUS:CONFIRMED SEQUENCE:0 LOCATION:B7 Room 3021 X-MICROSOFT-CDO-APPT-SEQUENCE:0 X-MICROSOFT-CDO-BUSYSTATUS:BUSY X-MICROSOFT-CDO-INTENDEDSTATUS:BUSY X-MICROSOFT-CDO-ALLDAYEVENT:FALSE X-MICROSOFT-CDO-IMPORTANCE:1 X-MICROSOFT-CDO-INSTTYPE:0 X-MICROSOFT-DONOTFORWARDMEETING:FALSE X-MICROSOFT-DISALLOW-COUNTER:FALSE X-MICROSOFT-REQUESTEDATTENDANCEMODE:DEFAULT X-MICROSOFT-ISRESPONSEREQUESTED:FALSE END:VEVENT BEGIN:VEVENT DESCRIPTION:This talk connects ideas from geometric group theory\, stochast ic processes\, and machine learning. We present a subtle Lipschitz result showing that for a norm-preserving group action\, a bound on the generatin g set induces a bound on distances between points within an orbit. We begi n with graph symmetry as a motivating example: the action of the permutati on group on vertices. We then prove our main result in the context of the general theory of stochastic orbit processes. Finally\, we explore connect ions to equivariance in machine learning.\n UID:040000008200E00074C5B7101A82E008000000008E3BA523C988DC01000000000000000 01000000053C82FFA5BD65743ACBD46230026EC22 SUMMARY:Spencer Goodfellow: Random group actions and stochastic orbit proce sses DTSTART;TZID=GMT Standard Time:20260216T120000 DTEND;TZID=GMT Standard Time:20260216T130000 CLASS:PUBLIC PRIORITY:5 DTSTAMP:20260810T024051Z TRANSP:OPAQUE STATUS:CONFIRMED SEQUENCE:0 LOCATION:54 / 10031 (10C) X-MICROSOFT-CDO-APPT-SEQUENCE:0 X-MICROSOFT-CDO-BUSYSTATUS:BUSY X-MICROSOFT-CDO-INTENDEDSTATUS:BUSY X-MICROSOFT-CDO-ALLDAYEVENT:FALSE X-MICROSOFT-CDO-IMPORTANCE:1 X-MICROSOFT-CDO-INSTTYPE:0 X-MICROSOFT-DONOTFORWARDMEETING:FALSE X-MICROSOFT-DISALLOW-COUNTER:FALSE X-MICROSOFT-REQUESTEDATTENDANCEMODE:DEFAULT X-MICROSOFT-ISRESPONSEREQUESTED:FALSE END:VEVENT BEGIN:VEVENT DESCRIPTION:For an infinite graph\, a periodic colouring of the vertices is one that is invariant under a subset of the symmetries of the graph. As s uch\, a natural consideration are those locally finite quasi-transitive gr aphs with finite quotient. Recent work from Abrishami and collaborators in vestigates whether all such graphs permit proper periodic colourings\, wit h conclusions dependent on the number of ends. An observation of Hopf tell s us any infinite locally finite\, quasi-transitive graph has 1\, 2\, or ∞-many ends. One case was left uncertain\; do all locally finite quasi-t ransitive planar graphs with 1-end permit a periodic colouring? In this ta lk I will review the results of Abrishami and collaborators before describ ing how\, through a theorem of Babai providing embeddings of 3-connected g raphs into the Euclidean or hyperbolic planes\, we can leverage properties of isometry groups to complete this investigation.\n UID:040000008200E00074C5B7101A82E008000000002CB9A764C988DC01000000000000000 01000000016AF89EA42C5D145849E3499641526DA SUMMARY:Luke Waite: Periodic colourings of 1-ended planar graphs DTSTART;TZID=GMT Standard Time:20260302T120000 DTEND;TZID=GMT Standard Time:20260302T130000 CLASS:PUBLIC PRIORITY:5 DTSTAMP:20260810T024051Z TRANSP:OPAQUE STATUS:CONFIRMED SEQUENCE:0 LOCATION:54 / 10031 (10C) X-MICROSOFT-CDO-APPT-SEQUENCE:0 X-MICROSOFT-CDO-BUSYSTATUS:BUSY X-MICROSOFT-CDO-INTENDEDSTATUS:BUSY X-MICROSOFT-CDO-ALLDAYEVENT:FALSE X-MICROSOFT-CDO-IMPORTANCE:1 X-MICROSOFT-CDO-INSTTYPE:0 X-MICROSOFT-DONOTFORWARDMEETING:FALSE X-MICROSOFT-DISALLOW-COUNTER:FALSE X-MICROSOFT-REQUESTEDATTENDANCEMODE:DEFAULT X-MICROSOFT-ISRESPONSEREQUESTED:FALSE END:VEVENT BEGIN:VEVENT DESCRIPTION:In 1966 Jane Matthews claimed that the conjugacy problem is sol vable in the standard restricted wreath product A \\wr B if and only if (i ) the conjugacy problem is solvable in A and B and (ii) B has a solvable p ower problem. We will discuss this result\, showing that an additional con dition is required - that either A is abelian or B has a solvable order pr oblem. We will also seek to extend this result to the permutational restri cted wreath product A \\wr_S B where\, rather than acting on itself\, B ac ts on a set S.\n UID:040000008200E00074C5B7101A82E00800000000E362E886C988DC01000000000000000 010000000A57042D36F26D1499EEC9A0245522363 SUMMARY:Sara Luder: The conjugacy problem in wreath products DTSTART;TZID=GMT Standard Time:20260316T120000 DTEND;TZID=GMT Standard Time:20260316T130000 CLASS:PUBLIC PRIORITY:5 DTSTAMP:20260810T024051Z TRANSP:OPAQUE STATUS:CONFIRMED SEQUENCE:0 LOCATION:54 / 10031 (10C) X-MICROSOFT-CDO-APPT-SEQUENCE:0 X-MICROSOFT-CDO-BUSYSTATUS:BUSY X-MICROSOFT-CDO-INTENDEDSTATUS:BUSY X-MICROSOFT-CDO-ALLDAYEVENT:FALSE X-MICROSOFT-CDO-IMPORTANCE:1 X-MICROSOFT-CDO-INSTTYPE:0 X-MICROSOFT-DONOTFORWARDMEETING:FALSE X-MICROSOFT-DISALLOW-COUNTER:FALSE X-MICROSOFT-REQUESTEDATTENDANCEMODE:DEFAULT X-MICROSOFT-ISRESPONSEREQUESTED:FALSE END:VEVENT BEGIN:VEVENT DESCRIPTION:In 1971\, Wilson introduced the structure lattice of a just-inf inite group and provided a classification of just-infinite groups based on it. In the late 1990s\, when Grigorchuk introduced the class of branch gr oups\, Wilson showed that the structure graph\, a subgraph of the structur e lattice\, encodes all the possible actions of a group as a branch group. This opened the door to the study of branch actions and\, in particular i t started the problem of classifying all the possible branch actions of a given branch group.\n\nIn this talk\, we generalize the notion of structur e graph from branch groups to weakly branch groups and show its applicatio ns to the study of the rigidity of weakly branch actions\, i.e. when the a ction of a group as a weakly branch group on a given tree is unique. We fu rther discuss applications to the first-order theory of weakly branch grou ps generalizing analogous results of Wilson for branch groups.\n\n UID:040000008200E00074C5B7101A82E0080000000010AA642C5FADDC01000000000000000 010000000BB1E9B91F97DC645A6C060EF17AEF07F SUMMARY:Jorge Fariña (Lund): Rigidity and first-order theory of weakly bra nch actions DTSTART;TZID=GMT Standard Time:20260427T120000 DTEND;TZID=GMT Standard Time:20260427T130000 CLASS:PUBLIC PRIORITY:5 DTSTAMP:20260810T024051Z TRANSP:OPAQUE STATUS:CONFIRMED SEQUENCE:0 LOCATION:54 / 10031 (10C) X-MICROSOFT-CDO-APPT-SEQUENCE:0 X-MICROSOFT-CDO-BUSYSTATUS:BUSY X-MICROSOFT-CDO-INTENDEDSTATUS:BUSY X-MICROSOFT-CDO-ALLDAYEVENT:FALSE X-MICROSOFT-CDO-IMPORTANCE:1 X-MICROSOFT-CDO-INSTTYPE:0 X-MICROSOFT-DONOTFORWARDMEETING:FALSE X-MICROSOFT-DISALLOW-COUNTER:FALSE X-MICROSOFT-REQUESTEDATTENDANCEMODE:DEFAULT X-MICROSOFT-ISRESPONSEREQUESTED:FALSE END:VEVENT BEGIN:VEVENT DESCRIPTION:The eigenvalues and eigenvectors of the graph Laplacian has a l ong history in computational harmonic analysis\, primarily utilised in cre ating local and global features of graphs. However\, the eigenvectors are known to be unstable under perturbations to the graph\, and subject to a c hoice of sign or basis in the eigenspace. Here\, we show that these two is sues can be solved by considering the projection-valued spectral measure o f the Laplacian. By construction\, it combines both eigenvalues and eigenv ectors into one coherent object\, and is independent of the choice of eige nbasis. Furthermore\, we prove that vertex features derived from the proje ction-valued spectral measure is Lipschitz stable with respect to perturba tions to the Laplacian\, which overcomes the instability of using eigenvec tors. We show that these vertex features empirically improve the performan ce of graph neural networks on graph regression tasks\, and can be used to detect approximate symmetries in point clouds and graphs.\n UID:040000008200E00074C5B7101A82E008000000009FA7688F5FADDC01000000000000000 010000000B3EA3042C4F6DB49B3B44D3DFDBE8616 SUMMARY:Ka Man Yim (Oxford): Stable and consistent spectral features of ver tices DTSTART;TZID=GMT Standard Time:20260511T120000 DTEND;TZID=GMT Standard Time:20260511T130000 CLASS:PUBLIC PRIORITY:5 DTSTAMP:20260810T024051Z TRANSP:OPAQUE STATUS:CONFIRMED SEQUENCE:0 LOCATION:54 / 10031 (10C) X-MICROSOFT-CDO-APPT-SEQUENCE:0 X-MICROSOFT-CDO-BUSYSTATUS:BUSY X-MICROSOFT-CDO-INTENDEDSTATUS:BUSY X-MICROSOFT-CDO-ALLDAYEVENT:FALSE X-MICROSOFT-CDO-IMPORTANCE:1 X-MICROSOFT-CDO-INSTTYPE:0 X-MICROSOFT-DONOTFORWARDMEETING:FALSE X-MICROSOFT-DISALLOW-COUNTER:FALSE X-MICROSOFT-REQUESTEDATTENDANCEMODE:DEFAULT X-MICROSOFT-ISRESPONSEREQUESTED:FALSE END:VEVENT BEGIN:VEVENT DESCRIPTION:Every odd positive integer admits a unique 3-smooth factorisati on\, and this talk develops that factorisation into a coordinate system th at partitions the nonnegative integers into countably many infinite triang les whose rows are Collatz chains of alternating parity. Within each trian gle\, the Collatz map becomes a deterministic diagonal flow\, with all num ber-theoretic difficulty concentrated at a single boundary. Inside this st ructure I will locate the Mersenne\, Thabit\, and Pierpont families\, and prove that an entire infinite family of rows in the principal skeleton con tains no primes\, the unique class of rows where elementary algebra alone forces every element to be composite. The framework is independent of the Collatz conjecture. I will close with what it does and does not say about the conjecture itself\, and open problems it raises.\n UID:040000008200E00074C5B7101A82E0080000000059BBB9DEB6D0DC01000000000000000 010000000E532CE69304B3A48964DF7B0DB125B82 SUMMARY:Jennifer Williams (Southampton): The Geometry of Collatz Chains: A Coordinate System from 3-Smooth Factorisation DTSTART;TZID=GMT Standard Time:20260601T120000 DTEND;TZID=GMT Standard Time:20260601T130000 CLASS:PUBLIC PRIORITY:5 DTSTAMP:20260810T024051Z TRANSP:OPAQUE STATUS:CONFIRMED SEQUENCE:0 LOCATION:04 / 4055 X-MICROSOFT-CDO-APPT-SEQUENCE:0 X-MICROSOFT-CDO-BUSYSTATUS:BUSY X-MICROSOFT-CDO-INTENDEDSTATUS:BUSY X-MICROSOFT-CDO-ALLDAYEVENT:FALSE X-MICROSOFT-CDO-IMPORTANCE:1 X-MICROSOFT-CDO-INSTTYPE:0 X-MICROSOFT-DONOTFORWARDMEETING:FALSE X-MICROSOFT-DISALLOW-COUNTER:FALSE X-MICROSOFT-REQUESTEDATTENDANCEMODE:DEFAULT X-MICROSOFT-ISRESPONSEREQUESTED:FALSE END:VEVENT END:VCALENDAR