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 metric spaces 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), 1195–1206
pdf with D.Fulghesu
19. Girth Alternative for subgroups of PL(I) Glasgow Mathematical Journal, 67, issue 1 (2025) 1-10.
pdf
20. A note on the problem of straight-line interpolation by ridge
functions,, Real Analysis Exchange, 50, issue 2, (2025), 267–278
pdf with V.Ismailov
21. Orientability of smooth manifolds, The Graduate Journal of Mathematics, 10, issue 2 (2025) 28-45.
pdf
22. On dense
subgroups of Homeo(I) pdf
23. Groups of diffeomorphisms of the
interval with finitely many fixed points pdf
24. Groups of homeomorphisms of the
interval with finitely many fixed points pdf
25. A new metric criterion for
non-amenability I
27. Finiteness of the topological rank of
diffeomorphism groups of compact manifolds. pdf
28. Non-bi-orderability of 6_2 and 7_6. with Cody Martin pdf
29. Examples of left-orderable and non-left-orderable
HNN extensions with Cody Martin pdf
30. Girth alternative for HNN extensions with Pratyush Mishra pdf
31. Non-biorderable one-relator groups without generalized torsion with James Thorne pdf
32. Big tiles in hyperbolic groups pdf
Refereed
for: 1. Annals of Mathematics 2. Journal of AMS (twice) 3.
Algebraic and Geometric Topology
4.
Osaka Journal of Mathematics 5.
Topology and its Applications
6.
Groups, Geometry and Dynamcis (twice)
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)
