Azer Akhmedov

NDSU Mathematics Department 


Interests: geometric group theory, Lie groups, ergodic theory, 3-manifolds, combinatorics.

Published papers:

1.  On the girth of finitely generated groups.  Journal of Algebra, 268, 2003, no.1, 198-208  

2. The girth of groups satisfying Tits Alternative. Journal of Algebra, 287, 2005, no.2, 275-282

3. Traveling salesman problem in groups. Contemporary Mathematics, vol.372, American Math. Soc. Providence, RI 2005.

4. Perturbations of wreath products and quasi-isometric rigidity I.  International Mathematics Research Notices (IMRN), vol.2008 (2008), (18 pages)

5.  On free discrete subgroups of Diff(I).  Algebraic and Geometric Topology, vol.10, no.4, (2010) 2409-2418. pdf

6.  Free limits of Thompson's group F. Geometriae Dedicata, vol.155, no.1, (2011) 163-176. with M.Stein and J.Taback pdf  

7. A weak Zassenhaus lemma for discrete subgroups of Diff(I) Algebraic and Geometric Topology, vol.14, no.1, (2014) 539-550. pdf

8. Chordal and timbral morphologies using Hamiltonian cycles. Journal of Mathematics and Music, vol.8, no 1, (2014), 1-24.  with M.Winter  pdf

9. Questions and remarks on discrete and dense subgroups of Diff(I). Journal of Topology and Analysis, vol. 6, no. 4, (2014), 557-571 pdf

10. Balance in random trees.  Open Journal of Discrete Mathematics, vol.4, no.4, (2014), 97-108. with W.Shreve pdf

11. Some applications of Holder's theorem in groups of analytic diffeomorphisms of one-manifolds  Topology and its Applications vol.180, (2015) 85-90. with M.Cohen  pdf

12. Good modulating sequences for the ergodic Hilbert transform. Turkish Journal of Mathematics vol.39 (2015) 124-138 with D.Comez  pdf

13. On the height of subgroups of Homeo(I) Journal of Group Theory vol. 18, no 1, (2015) 93-108 pdf

14. Cayley graphs with an infinite Heesch number.  The Electronic Journal of Combinatorics. vol.23 (1) 2016. pdf

15.  Extension of Holder's Theorem in Diff^{1+\epsilon }(I) Ergodic Theory & Dynamical Systems  vol.36, no 5, (2016), 1343-1353. pdf

16. Groups not acting on Compact MetricSpaces by Homeomorphisms  New York Journal of Mathematics, vol 23, 2017, 1321-1325. pdf

17. Existence and genericity of finite topological generating sets for homeomorphism groups.  Indiana University Mathematics Journal, 68 (2019) 1833-1848.  pdf  with M.Cohen 

18. Arithmetic sets in groups,   Mathematische Zeitschrift, 292(2019), 11951206  pdf with Damiano Fulghesu 

Preprints and work in progress:

19. Girth alternative for subgroups of PL(I) pdf

20. On dense subgroups of Homeo(I) pdf

21. Groups of diffeomorphisms of the interval with finitely many fixed points I pdf

22. Groups of diffeomorphisms of the interval with finitely many fixed points II pdf

23. Amenable subgroups of Homeo(R) with large characterizing quotients. pdf

24. A new metric criterion for non-amenability I

25. Roots of homeomorphisms: existence, uniqueness and convergence with M.Cohen and D.Comez

26. Finiteness of the topological rank of diffeomorphism groups of compact manifolds. pdf

27. Non-bi-orderability of 6_2 and 7_6. with Cody Martin  pdf


Refereed for: 1. Annals of Mathematics   2. Journal of AMS   3. Algebraic and Geometric Topology   4. Osaka Journal of Mathematics   5. Topology and its Applications   6. Groups, Geometry and Dynamcis   7. Contemporary Mathematics. 8. Open Journal of Discrete Mathematics  9. Annales de Tolouse

Besides, I have refereed several (at least three) well known unsubmitted preprints.


Reviewer for Zentralblatt. 


 Undergraduate Courses:

1.  Calculus I (Yale, NDSU)

2. Calculus II (Yale)

3. Calculus III (Yale, UCSB, NDSU)

4. Calculus for Social and Life Sciences (UCSB)

5. Linear Algebra (NDSU)

6. Introduction to Differential Equations (UCSB, NDSU)

7. Transition to a higher mathematics/Abstract Mathematics (UCSB, NDSU)

8. Combinatorics (UCSB)

9. Introduction to Group Theory (UCSB)

10. Real Analysis (UCSB, NDSU)

11. Introduction to Topology (NDSU)

12. Metric Space Topology (NDSU)

13. Introduction to Graph Theory (UCSB)

14. Introduction to Number Theory I, II (UCSB)

15. Complex Analysis (NDSU)

16. Differential Geometry (NDSU)


Graduate Courses:

17. Algebraic Topology (NDSU)

18. Introduction to Differential Topology (NDSU)

19. Topics in Smooth Dynamics (NDSU)

20. Topics in Lie Groups (NDSU)

21. Introduction to Riemannian Geometry (NDSU)

22. Introduction to Knot Theory (NDSU)

23. 3-manifolds (NDSU)

24. Lattices of Lie groups (NDSU)

25. Groups and Fractals (reading course, NDSU)

26. Knot Groups (reading course, NDSU)




Math Club

Math Humor

My Favorite Things


My Favorite Things (Math)


 Ph.D Students:

Cody Martin (Ph.D. May 2020)

Pratyush Mishra (Ph.D August 2023), Visiting Assistant Professor at Wake Forest Universty

James Thorne (Ph.D expected by Dec.2024) Instructor, Minnesota State University, Mankato

Wesley Voley

 Master's Degree Students:

Brandon Allen (M.S. December 2022)


Postdoctoral Mentorship:

Michael Cohen, NDSU (2014-2016)


Pictures: 1  2  3  4