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 teaching
**Math 582/428,**a course on homological and commutative algebra, at the University of Alberta. Students in this course can find information about this course on eClass. - I am currently organizing the Number Theory Seminar at the University of Alberta.

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]