I am a mathematician working primarily in algebra and arithmetic / algebraic geometry. My research interests mostly revolve around Galois theory, with an emphasis on anabelian geometry and other related topics in arithmetic/algebraic geometry. I am also interested in various other topics, such as algebraic cycles, Hodge theory (Archimedean and p-adic), valuation theory, differential Galois theory, model theory of fields, etc.

I am currently an Assistant Professor in the department of Mathematical and Statistical Sciences at the University of Alberta. I previously held postdoctoral positions at Oxford and Berkeley. I completed my Ph.D. in 2013 at the University of Pennsylvania.

The best way to contact me is through email. My address follows the following format:

`{surname}@u{Canadian province}.ca`

Replace {foo} as necessary, and don’t forget the “u” after the “at” symbol. Use only lowercase characters.

```
Mathematical and Statistical Sciences
University of Alberta
632 Central Academic Building
Edmonton, Alberta
Canada T6G 2G1
```

My papers are all available on the arXiv. Here is my listing on mathscinet.

- F. Pop and A. Topaz.
*A linear variant of GT.*arXiv - A. Topaz.
*Recovering function fields from their integral ℓ-adic cohomology with the Galois action.*arXiv - A. Topaz.
*A Torelli Theorem for Higher-Dimensional Function Fields.*arXiv

- J. Bell, R. Moosa and A. Topaz.
*Invariant Hypersurfaces.*To appear in J. Inst. Math. Jussieu (2020). arXiv DOI - P. Guillot, J. Mináč and A. Topaz. Appendix by O. Wittenberg.
*Four-fold Massey products in Galois cohomology.*Compositio Mathematica (2018) 154 (9), 1921-1959. arXiv DOI - A. Topaz.
*The Galois action on geometric lattices and the mod-ℓ I/OM.*Invent. Math. (2018) 213 (2), 371-459. Journal (open) - A. Topaz.
*Abelian-by-Central Galois Groups I: A Formal Description.*Trans. Amer. Math. Soc. (2017) 368, pg. 2721-2745. arXiv Journal - A. Topaz.
*Commuting-Liftable Subgroups of Galois Groups II.*J. reine angew. Math. (2017) 730, pg. 65-133. arXiv Journal - A. Topaz.
*Reconstructing Function Fields from Rational Quotients of Mod-ℓ Galois Groups.*Math. Annalen (2016) 366 (1), Pg. 337-385. arXiv Journal - A. Topaz.
*Abelian-by-Central Galois Groups II: Definability of Inertia / Decomposition Groups.*Israel J. Math. (2016) 215 (2), Pg. 713-748. arXiv - A. Topaz.
*On the Nature of Base Fields.*Appendix in ‘On The Minimized Decomposition Theory of Valuations’ by F. Pop, Bull. Math. Soc. Sci. Math. Roumanie. Tome 58(106) No. 3. Journal - J. Mináč, J. Swallow and A. Topaz.
*Galois Module Structure of ℤ/ℓ*Bull. London Math. Soc. (2014) 46 (1), Pg. 143-154 arXiv Journal^{n}-th Classes of Fields.

- A. Topaz.
*A linear variant of GT (joint with F. Pop).*In Overwolfach Reports: Homotopic and Geometric Galois Theory (2021). - A. Topaz.
*On the (generic) cohomology of function fields.*In Overwolfach Reports: Field Arithmetic (2018). - A. Topaz.
*On Milnor K-groups of Function Fields.*In Oberwolfach Reports: Valuation Theory and its Applications (2014). - A. Topaz.
*Detecting Valuations Using Small Galois Groups.*Valuation Theory in Interaction (Proceedings of the 2nd International Conference on Valuation Theory). Link - A. Topaz.
*Pro-ℓ Galois groups and valuations.*In Oberwolfach Reports: Arithmetic of Fields (2013). - A. Topaz.
*Commuting-liftable subgroups of Galois groups.*Ph.D. Thesis at the University of Pennsylvania (2013). Link - A. Topaz.
*Almost-commuting-liftable subgroups of Galois groups.*Manuscript (2012). Will not be submitted for publication. arXiv