HTML and/or PDF files in the folder talklist-mt
For an html and pdf (or ppt) file with the same name, the html is an exposition. Click on any of the [ 11] items below.
An unclickable "Pending" is still in construction. Use [ Comment on ...] buttons to respond to each item, or to the whole page at the bottom.

✺ Five talks given in London, Ontario, October 2005, The pdf file contains the abstracts of the talks. Click on titles for the actual talks:

• Dihedral Groups: Cusps on modular curves from MT viewpoint
• Alternating groups: Role of g-p' Cusps
• Cryptography and Schur's Conjecture
• Limit groups: Mapping class orbits and maximal Frattini quotients of dim. 2 p-Poincaré dual groups
• Galois closure groups: Outline proof of the Main Conjecture for r = 4; variants of the Regular Inverse Galois Problem; Serre's Open Image Theorem

MTabstracts09-04-05LO.pdf

✺ Dihedral Groups: MT view of Modular curve cusps London, Ont., Talk 1, Oct. 17, 2005, revised extensively for Istanbul, June 17, 2008. While cusps of modular curves are special among those for general Modular Towers, understanding general cusps has benefited from using the M(odular)T(ower) viewpoint to see modular curve cusps. Modular curve cusps have just two types, g-p', and p-cusps: the 3rd type, o-p' is missing. In good cases, as with alternating groups replacing dihedral groups, and the prime p=2, where the o-p' disappear at level 1, we aren't surprised that a modular curve-like uniformity of cusps sets in at higher levels. In both cases H(arbater)-M(umford) cusps and their shifts capture much information. App. E₁ illustrates how to use the sh-incidence cusp pairing on reduced Hurwitz spaces by computing it for the curves X_j(p²), j=0, 1. London1-ModCurves.html %-%-% London1-ModCurves.pdf

✺ Regular realizations of p-projective quotients and modular curve-like towers, Talk at the pro-p profinite Group Theory Conference 05/25/06 in Oberwolfach Germany. An exposition on Modular Towers and its relation to the Strong Torsion Conjecture of Abelian Varieties: mfried-ow05-25-06.html %-%-% mfried-ow05-25-06.pdf

✺ How Pure-cycle Nielsen classes test the Main Modular Tower Conjecture, Talk on 10/26/06 RIMS Conference on Profinite Arithmetic Geometry. An exposition of how the "Fried-Serre" lifting invariant finds 2 cusps whose existence gives the Main MT Conjecture: rims-fried10-26-06.html %-%-% rims-fried10-26-06.pdf

✺ Connectedness of moduli spaces of Riemann Surface covers, Talk given in the Eisenbud-Osserman seminar at Berkeley, 10/17/07: Berk-connMod10-17-06.html %-%-% Berk-connMod10-17-06.pdf

✺ Maximal Frattini quotients of p-Poinare Duality Groups, at Davidson AMS meeting on 03/03/07, Davidson N. Carolina. Has a completely group theoretic formulation of the Main Conjecture of Modular Towers, and examples that are serious tests for the Strong Torsion Conjecture: amsdav03-03-07FratpPoin.pdf

✺ Finite group theory and Connectedness of moduli spaces of Riemann Surface covers, Colloquium Talk at Univ. of Michigan, 03/27/07. The talk failed at UM because no group theorists showed, and it was primed for them. We will try this one again elsewhere: michcoll03-27-07.html %-%-% michcoll03-27-07.pdf

✺ Atomic Orbital-type cusps on Alternating Group Modular Towers, talk in the session Applicatons of Algebraic Stacks, Western Ontario Canada, 8-10 December, 2007. The MT goal: Show the sh-incidence (cusp pairing) matrix in action applied to infinitely many MTs (starting from a connectedness result of Liu and Osserman) where the Main Conjectures are proved: lonOnt12-08-07.html %-%-% lonOnt12-08-07.pdf

✺ Updating an Abel-Gauss-Riemann Program, UC Irvine colloquium, May 22, 2008: Riemann produced many tools that allow generalizing Abel's production of modular curves. A missing ingredient was how to generalize Galois' introduction and analysis of the higher level curves we call X₀(p^k+1), k≥ 0. While Shimura's projects are related, they don't capture the most useful part of Riemann's program. Using moduli spaces of covers requires deducing properties of the spaces from their cusps. New techniques for identifying cusps of Hurwitz spaces combine with connectedness results to identify advantageous cusps. Our applications here show modular curve-like properties for Modular Towers over alternating group Hurwitz spaces. ucicoll05-22-08.html %-%-% ucicoll05-22-08.pdf

✺ Conway-Fried-Parker-Voelklein connectedness results London, Ont., Talk 2, Oct. 18, 2005, revised extensively for Istanbul, June 19, 2008. By combining Clebsch's result from 1872 on 2-cycle Nielsen classes with my use of the Spin lifting invariant for describing connected components of 3-cycle Nielsen classes, we see the rational for the CFPV Theorem. Also, how to improve it so it extends all the classical results. The talk includes the full definition of g-p' representative. When conjugacy classes are repeated suitably often, there will be but one component containing g-p' reps., that will be defined over Q, and application of the theorem avoids special knowledge of Schur multipliers. London2-AltGps.html %-%-% London2-AltGps.pdf

✺ Istanbul Summer School 9–20 June 2008, Geometry and Arithmetic of Moduli Spaces of Coverings.

1. Preliminary tools and working knowledge
2. Construction of moduli spaces and stacks of coverings (Hurwitz spaces)
3. Geometry and arithmetic of moduli spaces of coverings
4. Connected Hurwitz space components and inverse Galois theory
5. Grothendieck-Teichmueller tower and Galois actions
6. Modular Towers

The colorful flyer indicates that even Turkish mathematicians are savvy to use their country's exotica. The html file gives the program subdivisions and the relation of the M(odular) T(ower) program and my three talks to the rest of that program. Istanbul06-09-08.html

For items above, use [Comment on ...] buttons after each. Click here to