The Department of Mathematics

Middlesex College

London, ON

Canada, N6A 5B7

Tel: 519.661.3639

Fax: 519.661.3610

Undergraduate inquiries:

math-inquiry@uwo.ca

Graduate inquiries:

math-grad-program@uwo.ca

All other inquiries:

mathdept@uwo.ca

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.

Selected Updates to Curriculum Vitae for 2015-2017

**THE BRAIN AND MIND INSTITUTE: **

Among my most recent interests belongs a strong additional research interest in the application of mathematics to the study of the brain. Fortunately at Western University we have the awesome Brain and Mind Institute. I am very excited about this new direction of my research which seems to have endless possibilities.

Canadian Mathematical Society Excellence in Teaching Award 2013

My three current PhD students are planning to graduate in 2019; therefore I am looking for new, enthusiastic, dedicated students; and I am also looking for further postdoctoral fellows.

Here at Western University in the Department of Mathematics, we have a wonderful, vital, enthusiastic team that is working feverishly on unveiling some of the exciting secrets of Galois theory and related topics in number theory, algebraic geometry, algebraic topology, analysis and geometry.

The considered topics are fascinating, and they range from classical to the most modern. There is strong collaboration with various mathematicians at Western, as well as worldwide.

Math 3150B - Elementary Number Theory (course outline)

Math 3121A / 9050A - Advanced Linear Algebra (course outline)

- 1) P. Guillot, J. Mináč and A. Topaz. Four-fold Massey products in Galois cohomology (with an Appendix by O. Wittenberg).
*Compositio Math.***154**(2018), no. 9, 1921-1959. - 2) J. Mináč and N. D. Tân. Triple Massey products and Galois theory.
*J. Eur. Math. Soc. (JEMS)***19**(2017), no. 1, 255-284. - 3) J. Mináč and N. D. Tân. Construction of unipotent Galois extensions and Massey products.
*Adv. Math.***304**(2017), 1021-1054. - 4) I. Efrat and J. Mináč. Galois groups and cohomological functors.
*Trans. Amer. Math. Soc.***369**(2017), no. 4, 2697-2720. - 5) M. Ataei, J. Mináč and N. D. Tân. Description of Galois unipotent extensions.
*J. Algebra***471**(2017), 193-219. - 6) J. Mináč and N. D. Tân. Counting Galois
**U**_{4}(**F**_{p})-extensions using Massey products.*J. Number Theory***176**(2017), 76-112. - 7) S. K. Chebolu, D. McQuillan and J. Mináč. Witt's cancellation theorem seen as a cancellation.
*Expo. Math.***35**(2017), no. 3, 300-314. - 8) J. Mináč and N. D. Tân. Triple Massey products vanish over all fields.
*J. Lond. Math. Soc. (2)***94**(2016), no. 3, 909-932. - 9) S. K. Chebolu, J. Mináč and A. Schultz. Galois
*p*-groups and Galois modules.*Rocky Mountain J. Math.***46**(2016), no. 5, 1405-1446. - 10) J. F. Carlson, S. K. Chebolu and J. Mináč. Ghosts and strong ghosts in the stable category.
*Canad. Math. Bull.***59**(2016), no. 4, 682-692. - 11) J. Mináč, M. Rogelstad and N. D. Tân. Dimensions of Zassenhaus filtration subquotients of some pro-
*p*-groups.*Israel J. Math*.**212**(2016), no. 2, 825-855. - 12) J. Mináč and N. D. Tân. Triple Massey products over global fields.
*Doc. Math*.**20**(2015), 1467-1480. - 13) S. K. Chebolu, J. Mináč and C. Quadrelli. Detecting fast solvability of equations via small powerful Galois groups.
*Trans. Amer. Math. Soc*.**367**(2015), no. 12, 8439-8464. - 14) J. Mináč and N. D. Tân (with an appendix written by I. Efrat, J. Mináč and N. D. Tân). The kernel unipotent conjecture and the vanishing of Massey products for odd rigid fields.
*Adv*.*Math*.**273**(2015), 242-270. - 15) P. Guillot and J. Mináč. Extensions of unipotent groups, Massey products and Galois theory (arXiv:1711.07711v2 [math.NT], 23 November 2017).
- 16) J. Mináč, F. W. Pasini, C. Quadrelli and N. D. Tân. Koszul algebras and quadratic duals in Galois cohomology (arXiv:1808.01695v1 [math.NT], 5 August, 2018).
- 17) J. Mináč, M. Rogelstad and N. D. Tân. Relations in the maximal pro-
*p*quotients of absolute Galois groups (arXiv:1808.01705v1 [math.NT], 6 August 2018). - 18) J. Mináč, M. Palaisti, F. W. Pasini and N. D. Tân. Enhanced Koszul properties in Galois cohomology (arXiv:1811.09272v1 [math.RA], 22 November 2018).

**Faculty of Science Distinguished Research Professorship 2004-2005.**

**Canadian Mathematical Society Summer Meeting 2018, Fredericton, NB. Co-organizer, Special Session: ***Cohomology - a link between numbers and geometry*, June 1-4, 2018*. *

**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 U _{4}(F_{p})-extensions using Massey products*, which is published in

**Poster **for an** Algebra Seminar talk** delivered, October 18, 2013, related to my joint work with N. D. Tân.

**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.

Some more papers related to my research may be found here. (See MathSciNet for a comprehensive list of my publications.)

April 1, 2019.**Invited Colloquium Speaker, Pure Mathematics Colloquium, University of Waterloo**,**Co-organizer, Special Session, Canadian Mathematical Society Summer Meeting**, Fredericton, New Brunswick, June 1-4, 2018. (Organized by S. Gille, J. Mináč and K. Zaynullin.)Nilpotent Fundamental Groups, June 18-23, 2017. (Organized by J. Mináč, F. Pop, A. Topaz and K. G. Wickelgren.)*Co-organizer, Banff International Research Station Workshop*:, Rutgers University.**2015 American Mathematical Society Fall Eastern Sectional Meeting**, University of Ottawa, June 8-10, 2013. Sponsored by the Fields Institute and organized by Damien Roy, University of Ottawa, and Cameron Stewart, University of Waterloo.*Workshop on Number Theory with a view towards Transcendence and Diophantine Approximation*, Carleton University, October 20-21, 2012. (Sponsored by the Fields Institute, the Ottawa-Carleton Institute for Algebra and Number Theory, and the School of Mathematics and Statistics, Carleton University.)*70th Algebra Days***IBG Advanced International School on Galois Groups**, Bilbao, Spain, July 2012.

*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.

I am also interested in Massey products, formality-like properties and Koszul properties of Galois cohomology, arithmetic geometry, Hodge theory, the section conjecture, the Langlands program, motivic cohomology, pefectoids, moduli spaces, Galois modules, and representation theory.

Recently I began together with my collaborators to investigate some novel approaches of mathematics to medicine.

(For some possible updates to my list of publications, please see my C. V. above.) Here are two more links to arXiv.org: (1) and (2).

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):

*Bernoulli Numbers and the Riemann Zeta Function,*by B. Sury*.*- The Continuing Story of Zeta, by G. Everest, Ch. Röttger and T. Ward.

Artist: Nikita Maria Findlay

- Ronie Peterson Dario (beginning September 2018)
- Federico W. Pasini (July 2017 - present)
- Michael Rogelstad (beginning September 2017)
- Nguyen Duy Tân (July 2018 - August 2018) and (July 2015 - August 2015)

- Ali Alkhairy
- Béatrice Chetard (co-supervised with P. Guillot - University of Strasbourg)
- Michal Cizek
- Marina Palaisti

- Milad Fakhari (2018 - present / co-supervised with D. Riley)

Here above is a link to MaCAW with some awesome graduate students with some great enthusiasm, excitement, and always interesting activities. I feel very privileged to work with some of them closely.