Igor Mineyev's Math Page

Igor Mineyev's Math Page.

"Mathematics is a piece of cake: if you like it, you will get it."

"My theory is that no matter how hard people try to describe the real world, any theory would give only a rough approximation to the reality. Except for my theory."

"...a point has the non-zero zero homology and the zero non-zero homology..."

--I.V.Mineyev, hope-not-yet-complete works.

I am an Associate Professor at UIUC Math Dept. My mathematical interests include subjects related to geometric group theory, in particular,

hyperbolic groups, metric geometry, flows, CAT(0) and CAT(-1) spaces,
the Hanna Neumann conjecture and generalizations,
the zero-divisors conjecture, the Atiyah problem,
various types of (co)homology of groups,
geometric and topological rigidity, conformal structures, geometric analysis,
3-manifolds, relative hyperbolicity,
the Novikov conjecture, the Baum-Connes conjecture,
and many other incoherent things...
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Teaching Math 595 now.

G³
homepage

I am an organizer of the annual G³ conference ("gee cube"). As y'all know, G³ stands for Geometric Group Theory on the Gulf Coast Conference, commonly abbreviated in various ways, for example, Geometric Groups on the Gulf.
The next G³ will take place in the spring of 2013.

Paper work.

l_infty-cohomology and metabolicity of negatively curved complexes. Internat. J. Algebra Comput. Vol. 9, No. 1(1999), 51-77.

Higher dimensional isoperimetric functions in hyperbolic groups. Math. Z. 233 (2000), no. 2, 327-345.

l₁-homology of combable groups and 3-manifold groups. International Conference on Geometric and Combinatorial Methods in Group Theory and Semigroup Theory (Lincoln, NE, 2000). Internat. J. Algebra Comput. 12 (2002), no. 1-2, 341-355.

Straightening and bounded cohomology of hyperbolic groups. GAFA, Geom. Funct. Anal. 11(2001), 807-839.

Bounded cohomology characterizes hyperbolic groups. Quart. J. Math. Oxford Ser., 53(2002), 59-73.

The Baum-Connes conjecture for hyperbolic groups. Joint with Guoliang Yu. Invent. Math. 149 (2002) 1, 97-122.

Ideal bicombings for hyperbolic groups and applications. Joint with N. Monod and Y. Shalom. Topology 43 (2004), no. 6, 1319-1344.

Non-microstates free entropy dimension for groups. Joint with D. Shlyakhtenko. GAFA, Geom. Funct. Anal., 15 (2005), 476-490.

Flows and joins of metric spaces. Geometry and Topology, Vol. 9 (2005), no. 13, 403-482. Here is how to type Latex symbols for this article. Also the file on GT web page.

Metric conformal structures and hyperbolic dimension. Conform. Geom. Dyn. 11 (2007), 137-163. Also the published version.

Relative hyperbolicity and bounded cohomology. Joint with A.Yaman. Preprint.

The topology and analysis of the Hanna Neumann Conjecture. J. Topol. Anal. (JTA), 3(2011), no. 3, 307-376.

Submultiplicativity and the Hanna Neumann Conjecture. Ann. of Math., 175 (2012), no. 1, 393-414. Also a latex leafage picture. Another leafage picture.

Groups, graphs, and the Hanna Neumann Conjecture. J. Topol. Anal. (JTA), 4(2012), no. 1, 1-12. Here is the pictures-only version of this article.

Miscellaneous

Funny math pictures at V.Troitsky's homepage. A very important statement.

A quote from teaching evaluations:
Instructor's weakness: high expectations. Freedom.

Another quote from teaching evaluations:
Do not teach proofs. They are useless. Teach what needs to be done on the homework and tests.

Paper work.
l_infty-cohomology and metabolicity of negatively curved complexes. Internat. J. Algebra Comput. Vol. 9, No. 1(1999), 51-77.
Higher dimensional isoperimetric functions in hyperbolic groups. Math. Z. 233 (2000), no. 2, 327-345.
l₁-homology of combable groups and 3-manifold groups. International Conference on Geometric and Combinatorial Methods in Group Theory and Semigroup Theory (Lincoln, NE, 2000). Internat. J. Algebra Comput. 12 (2002), no. 1-2, 341-355.
Straightening and bounded cohomology of hyperbolic groups. GAFA, Geom. Funct. Anal. 11(2001), 807-839.
Bounded cohomology characterizes hyperbolic groups. Quart. J. Math. Oxford Ser., 53(2002), 59-73.
The Baum-Connes conjecture for hyperbolic groups. Joint with Guoliang Yu. Invent. Math. 149 (2002) 1, 97-122.
Ideal bicombings for hyperbolic groups and applications. Joint with N. Monod and Y. Shalom. Topology 43 (2004), no. 6, 1319-1344.
Non-microstates free entropy dimension for groups. Joint with D. Shlyakhtenko. GAFA, Geom. Funct. Anal., 15 (2005), 476-490.
Flows and joins of metric spaces. Geometry and Topology, Vol. 9 (2005), no. 13, 403-482. Here is how to type Latex symbols for this article. Also the file on GT web page.
Metric conformal structures and hyperbolic dimension. Conform. Geom. Dyn. 11 (2007), 137-163. Also the published version.
Relative hyperbolicity and bounded cohomology. Joint with A.Yaman. Preprint.
The topology and analysis of the Hanna Neumann Conjecture. J. Topol. Anal. (JTA), 3(2011), no. 3, 307-376.
Submultiplicativity and the Hanna Neumann Conjecture. Ann. of Math., 175 (2012), no. 1, 393-414. Also a latex leafage picture. Another leafage picture.
Groups, graphs, and the Hanna Neumann Conjecture. J. Topol. Anal. (JTA), 4(2012), no. 1, 1-12. Here is the pictures-only version of this article.

Miscellaneous
Funny math pictures at V.Troitsky's homepage.	A very important statement.
A quote from teaching evaluations: *Instructor's weakness: high expectations.*	Freedom.
Another quote from teaching evaluations: *Do not teach proofs. They are useless. Teach what needs to be done on the homework and tests.*

Department of Mathematics
University of Illinois at Urbana-Champaign
250 Altgeld Hall
Urbana, IL 61801, USA

Email address: mineyev math uiuc edu