Department of Mathematics
Louisiana State University
Baton Rouge, LA 70803-4918
Office: 140 Lockett Hall
I am a Postdoctoral Researcher in the Department of Mathematics at Louisiana State University
working with Pallavi Dani. I received Ph.D. from the
University of Oklahoma in May 2018 under the supervision of Noel Brady.
Geometric group theory and low-dimensional topology, with emphasis on right-angled Artin
groups, free-by-cyclic groups, CAT(0) cube complexes, Dehn functions of groups and stable commutator length. I also
have an ongoing interest in mapping class groups, profinite groups and criteria for linearity.
Published papers and preprints:
Realizable ranks of joins and intersections of subgroups in free groups. arXiv:1901.04463
We describe the locus of possible ranks ( rk (H v K), rk(H\cap K) ) for any given subgroups H, K of a free group.
In particular, we prove the remaining open case (m=4) of R.Guzman's ``Group-Theoretic Conjecture'' conjecture.
Uncountably many quasi-isometry classes of groups of type FP.
(with R. Kropholler and I. Leary)
arXiv:1712.05826. Accepted in the American Journal of Mathematics.
We prove that among I. Leary's groups of type FP there exist uncountably many non-quasi-isometric ones.
We also prove that for each n>3 there exist uncountably many quasi-isometry classes of non-finitely presented n-dimensional Poincare duality groups.
Slides from the talk at the University of Bielefeld.
Genus bounds in right-angled Artin groups.
(with M. Forester and J. Tao)
arXiv:1710.10542. Accepted in Publicacions Matemàtiques.
We generalize Culler's proof for the lower bound for the stable commutator length in free groups to the case of right-angled Artin groups.
Slides from the talk at the University of Auburn.
Dehn functions of subgroups of right-angled Artin groups.
(with N. Brady) Geometriae Dedicata (2018).
We show that polynomials of arbitrary integer degree are realizable as Dehn functions of subgroups in right-angled Artin groups.
Linearity criteria for poly-free groups, pdf.
In his article on what is now called 'Lubotzky's linearity criterion',
Alexander Lubotzky established a criterion for a group Aut(F) to be
linear, where F is a free group of finite rank in terms of
'p-congruence systems'. We generalize this result of his to the case of
groups of the form A(semidirect)F, where A is a finitely generated
subgroup of Aut(F).
Presentations and Linearity of Some Low Genus Mapping Class Groups,
In this expository note we show that the pure mapping class group of
the surface of genus g, with b boundary components and n punctures
is linear for the following values of (g,b,n): (1,2,0), (1,1,1), (1,0,2), (1,3,0), (1,2,1), (1,1,2), (1,0,3).
- On a question of Peter Sarnak, pdf.
In his 2012 MSRI "Notes on thin groups" Peter Sarnak asks if a
specific pair of symplectic matrices generates an infinite index
subgroup in Sp(4,Z). We approach this question with a technique adapted
from mapping class groups.
In Spring 2019 I am not teaching.
In Fall 2018 I was teaching Math 1550 section 37, Calculus and Analytic Geometry
Previous teaching in the University of Oklahoma:
- Spring 2018, Fall 2017: not teaching - Research Assistant with Dr. Jing Tao.
- Spring 2017: Lecturer for Calculus-I (small class).
- Fall 2016: On leave to MSRI.
- Spring 2016: Lecturer for Calculus-III (small class).
- Spring, Fall 2015: Two discussion sections for Calculus-I (accelerated) class.
- Fall 2014: Discussion section for Calculus-III (Honors) class.
- In Fall 2014 I was awarded with the Provost Certificate of Distinction in Teaching.
- Spring 2014: Discussion section for Calculus-II (Honors) class
- Fall 2013: Two discussion sections for Calculus-II class.
My wife Hayat Hokayem is an Associate Professor at the College of Education in Texas Christian University, Fort Worth, TX.
Our son Vikenty (born in August 2014): 1, 2, 3, 4,
Our son Nikolai (born in June 2017): 1, 2,
3, 4, 5.
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This page was last updated on Friday, January 18, 2019.