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**.

- I am currently organizing the Number Theory Seminar at the University of Alberta.
- I am currently teaching
**Math 324, Elementary Number Theory**at the University of Alberta. Students in this course can find information about this course on eClass.

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
```

Most of my papers are available on the arXiv.

**Recovering function fields from their integral ℓ-adic cohomology with the Galois action.**

*By A. Topaz.*ArXiv manuscript (2019).**Links:**[arXiv]**Invariant Hypersurfaces.**

*By J. Bell, R. Moosa and A. Topaz.*ArXiv manuscript (2018).**Links:**[arXiv]**A Torelli Theorem for Higher-Dimensional Function Fields.**

*By A. Topaz.*ArXiv manuscript (2017).**Links:**[arXiv]

**Four-fold Massey products in Galois cohomology.**

*By P. Guillot, J. Mináč and A. Topaz, with an appendix by O. Wittenberg.*Compositio Mathematica (2018) 154 (9), 1921-1959.**Links:**[arXiv] [Journal]**The Galois action on geometric lattices and the mod-ℓ I/OM.**

*By A. Topaz.*Invent. Math. (2018) 213 (2), 371-459.**Links:**[Journal (open)]**Abelian-by-Central Galois Groups I: A Formal Description.**

*By A. Topaz.*Trans. Amer. Math. Soc. (2017) 368, pg. 2721-2745.**Links:**[arXiv] [Journal]**Commuting-Liftable Subgroups of Galois Groups II.**

*By A. Topaz.*J. reine angew. Math. (2017) 730, pg. 65-133.**Links:**[arXiv] [Journal]**Reconstructing Function Fields from Rational Quotients of Mod-ℓ Galois Groups.**

*By A. Topaz.*Math. Annalen (2016) 366 (1), Pg. 337-385.**Links:**[arXiv] [Journal]**Abelian-by-Central Galois Groups II: Definability of Inertia / Decomposition Groups.**

*By A. Topaz.*Israel J. Math. (2016) 215 (2), Pg. 713-748.**Links:**[arXiv]**On the Nature of Base Fields.**

*By A. Topaz.*Appendix in ‘On The Minimized Decomposition Theory of Valuations’ by F. Pop, Bull. Math. Soc. Sci. Math. Roumanie. Tome 58(106) No. 3.**Links:**[Journal]**Galois Module Structure of ℤ/ℓ**^{n}-th Classes of Fields.

*By J. Mináč, J. Swallow and A. Topaz.*Bull. London Math. Soc. (2014) 46 (1), Pg. 143-154.**Links:**[arXiv] [Journal]

**On the (generic) cohomology of function fields.**

*By A. Topaz.*In Overwolfach Reports: Field Arithmetic (2018).**On Milnor K-groups of Function Fields.**

*By A. Topaz.*In Oberwolfach Reports: Valuation Theory and its Applications (2014).**Detecting Valuations Using Small Galois Groups.**

*By A. Topaz.*Valuation Theory in Interaction (Proceedings of the 2nd International Conference on Valuation Theory). [Link]**Pro-ℓ Galois groups and valuations.**

*By A. Topaz.*In Oberwolfach Reports: Arithmetic of Fields (2013).**Commuting-Liftable Subgroups of Galois Groups.**

*By A. Topaz.*Ph.D. Thesis at the University of Pennsylvania (2013). [Link]**Almost-commuting-liftable subgroups of Galois groups.**

*By A. Topaz.*Manuscript (2012). Will not be submitted for publication. [arXiv]