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Personal profile


I am a Reader in Pure Mathematics at the University of Manchester. My research area is Differential Geometry,  Topology, and Mathematical Physics. I have done research in supermanifold geometry, quantization, index theorem, quantum groups, and integral geometry. My most recent research concerns topics such as odd and even Poisson brackets, geometry of differential operators, homotopy algebras, super linear algebra and its applications, and others. You can find more information here.

Since 1991 till 1996, I taught at the Department of Mathematics of the Moscow State University. Before coming to Manchester in February 1999, I had spent some good time in California at the UC Berkeleyand (briefly) at the UCSD. I have been back at Berkeley a few times as a visiting scholar after moving to Manchester.

I obtained my Ph.D. and B.A./M.A. from the Moscow State University in 1989 and 1984. Moscow is my native place and my mother tongue is Russian. I consider myself as a member of the large community of Russian mathematicians working outside Russia.  Besides mathematics, I am interested in literature, religion, and philosophy.


PhD (1989) and BA/MA (1984) from the Department of Mathematics of the Moscow State University 

Research interests

Much of what I do is related with supermanifolds and their applications. Broad areas of recent research can be described as bracket geometry (which includes odd and even Poisson structures, Lie algebroids and their generalizations, and homotopy algebras), geometry of differential operators, and integration on supermanifolds.

Some earlier "best results": (1) de Rham theory for supermanifolds, discovery of new "variational" differential and links with Gelfand's general hypergeometric equations and integral geometry; (2) higher derived brackets, with applications to graded manifolds, homological vector fields, and Batalin-Vilkovisky geometry; (3) universal recurrence relations for super exterior powers, new formula for Berezinian as ratio of polynomial invariants, and applications to Buchstaber-Rees theory of n-homomorphisms (joint with H. Khudaverdian);

Current interests include analytic formulas for volumes of classical supermanifolds, microformal geometry and homotopy algebras, and super Darboux transformations.

You can find more information here

I am in charge of the Manchester Geometry Seminar (together with my friend and collaborator Dr Hovhannes Khudaverdian, Prof. Nigel Ray, Dr Hendrik Suess and Dr James Montaldi).  

My group


I supervise PhD students together with my friend and collaborator Dr Hovhannes Khudaverdian. We had jointly supervised Dr Adam Haunch (PhD, 2007), Mr Paul Physick (MPhil, 2008), Mr Graham Kemp (MSc, 2010), Dr Andrew Bruce (PhD, 2009),  Dr Jacob George (MSc, 2006, and PhD, 2009),  Dr Rabah Djabri (PhD, 2011), Dr Adam Biggs (PhD, 2014), and Dr Matthew Peddie (PhD, 2017).
We have  one current and one perspective (starting Sept 2019) PhD students.

We invite students for PhD studies in the broad area of Geometry and Mathematical Physics.  There are many research projects that we can offer. Please get in touch with us. You may also find useful the link to the School postgraduate admission web page. 

I have also taught a postgraduate course on geometry of fiber bundles and have supervised various level projects on topics including de Rham and Čech cohomology, characteristic classes, and other areas of differential geometry.


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