Here is a joint survey paper written with Sunil Chebolu and Dan McQuillan, with illustrations by Matthew Teigen. It was great fun to work on this paper, and we only hoped that it would also be interesting and stimulating for the reader as well. It has been therefore rewarding to receive some very nice responses from our colleagues related to this paper.
Banff International Research Station Workshop on Nilpotent Fundamental Groups, June 18 - 23, 2017. Organizers: J. Mináč, F. Pop, A. Topaz and K. G. Wickelgren.
Here is a link to a short video abstract about my paper with Nguyễn Duy Tân, entitled: Counting Galois U4(Fp)-extensions using Massey products, which is published in J. Number Theory (see (5) in the list of 2017 publications above).
Here is a nice paper entitled: Étude Kummerienne de la q-suite Centrale Descendante d'un Groupe de Galois, by Professor T. Nguyen Quang Do, related to my joint work with S. K. Chebolu, I. Efrat, and M. Spira; as well as to the work of R. Sharifi and others. (Please allow a minute or so to load this document for viewing.) Here is a faster link going directly to this paper.
Here is another nice paper by Professors F. Bogomolov and Y. Tschinkel entitled: Introduction to birational anabelian geometry in Current Developments in Algebraic Geometry (L. Caporaso, J. McKernan, M. Mustata, M. Popa, editors), pages 17-63, MSRI Publications, Volume 59, Cambridge University Press, 2012. (This is a great description of this exciting area, and it includes some of my work with S. K. Chebolu and I. Efrat.)
In the paper, Multiquadratic extensions, rigid fields and Pythagorean fields, D. Leep and T. L. Smith obtained some rather elegant, new proofs of some theorems which I published with A. Adem, W. Gao and D. Karagueuzian in 2001; and also with T. L. Smith in 2000.
This paragraph is still "under construction" --- Three talks were delivered by A. Topaz at an exciting University of Pennsylvania Galois Seminar in 2009-2010 and 2012-2013. The first two talks delivered in 2009 concern my paper co-authored with S. K. Chebolu and I. Efrat, published in Math. Ann. (Quotients of absolute Galois groups which determine the entire Galois cohomology, Volume 352 (2012), no. 1, 205-221.) At the time of these seminars, this paper was not yet published, but it was posted on the arXiv. The second talk (November 4, 2009) was available on video, but it is not clear if now in 2018 this video is still available. The third talk (November 2, 2012) is concerning my joint work with A. Topaz and J. Swallow, and its subsequent continuation with A. Topaz. The first paper is on the arXiv and the second paper is a 'work in progress'.
Algebraic Number Theory, Galois Cohomology, Quadratic Forms, Field Theory, Brauer Groups, Algebraic K-Theory, Algebraic Geometry, and Algebraic Topology.
The Bloch-Kato conjecture, quadratic forms, Galois groups and Galois cohomology, Grothendieck's anabelian geometry, zeta functions, analytic pro-p groups, algebraic K-theory, cohomology of finite p-groups, Galois groups of maximal p-extensions with a given set of ramification points, the stable homotopy category, and Freyd's generating hypothesis. I am also very interested in both the finite generation of Tate cohomology and Lie algebras associated with Galois groups.
Here are some cool and interesting survey papers on some elementary aspects of the values of the zeta function, where the authors also refer to my observation (A Remark on the Values of the Zeta Function, Expo. Math. 12 (1994), 459-462):
Artist: Nikita Maria Findlay
Relentless pursuit of mathematical adventures