Pavel Mnev
Department of Mathematics
University of Notre Dame
255 Hurley
Notre Dame, IN 46556
I am an assistant professor at the math department of the
University of Notre Dame. Here is my CV.
Research Interests:
My research is in mathematical physics, more
precisely I am interested in the interactions of quantum
field theory with topology, homological/homotopical
algebra and supergeometry.
One important homological algebra technique that allows
one to construct mathematically the path integral
quantization of gauge theories (and, in particular,
topological field theories) is the BatalinVilkovisky
formalism. E.g. for a class of topological field theories
(the socalled AlexandrovKontsevichSchwarzZaboronsky
sigma models) it leads to quantum partition functions
expressed in terms of (finitedimensional) integrals over
FultonMacPherson compactified configuration spaces of
points on a manifold which constitute interesting manifold
invariants compatible with gluingcutting.
Some questions I am interested in:
Constructing exact discretizations of topological field
theories on manifolds endowed with CW decompositions.
Comparison of perturbative results in quantum field
theory with nonperturbative ones, via the globalization
procedure (relying on techniques of formal geometry) on
the moduli space of solutions to EulerLagrange equations.
Extending the perturbative path integral construction of
quantum field theory to manifolds with corners of
codimension 2 and higher, and comparing with
BaezDolanLurie framework of (fully) extended topological
quantum field theory.
"Secondary" renormalization flow in topological field
theory and IgusaKlein higher torsions.
How does renormalization in nontopological field
theories interact with gluing/cutting?
Publications and
preprints:
 P. Mnev, "Towards
simplicial ChernSimons theory, I" an unpublished
draft (2005), here.
We consider the problem of discretizing topological
field theories of Chern Simons type. Our main instruments
are BatalinVilkovysky formalism and standard Feynman
diagram technique for functional integral in QFT. We solve
the 1dimensional case of the problem completely and check
that the result does not exhibit nontrivial renormalization.
Then we face the 2dimensional case of discretizing theory
on a triangle. We use Dupont construction for choosing the
gauge and find the action of the discretized theory in
lowest nontrivial order (containing higher classical and
quantum operations). Next we check (by direct calculations,
in lowest nontrivial order) that this action does possess
nontrivial topological (BVexact) renormalization flow for
quantum operations under barycentric gluing, while classical
operations are recovered.
 P. Mnev, "On the
simplicial BF model," J. Math. Sci. 141, 4 (2007)
14291431.
 P. Mnev, "Discrete path
integral approach to the trace formula for regular graphs",
Commun. Math. Phys. 274.1 (2007) 233241, arXiv:mathph/0609028.
We give a new proof of the trace formula for regular
graphs. Our approach is inspired by path integral approach
in quantum mechanics, and calculations are mostly
combinatorial.
 P. Mnev, "Notes on
simplicial BF theory", Moscow Math. J 9.2 (2009)
371410, arXiv:hepth/0610326.
In this work we discuss the construction of "simplicial
BF theory", the field theory with finitedimensional space
of fields, associated to a triangulated manifold, that is in
a sense equivalent to topological BF theory on the manifold
(with infinitedimensional space of fields). This is done in
framework of simplicial program  program of constructing
discrete topological field theories. We also discuss the
relation of these constructions to homotopy algebra.
 P. Mnev, "On simplicial BF
theory," Russian Academy of Sciences, Doklady
Mathematics 77.1 (2008) 5963. English translation. Original Russian version.
In this note we outline the construction of simplicial
BF theory on a triangulated manifold as a special case of
the construction of effective action for the abstract BF
theory by means of a BatalinVilkovisky
integral. We present our results for the simplicial action
as closed formulae in dimensions 0 and 1 and as perturbative
answers in higher dimension. We explain the action of
simplicial BF theory in terms of homotopy transfer of
algebraic structures.
 P. Mnev, "Discrete BF theory,"
arXiv:0809.1160
[hepth] (the English translation of my
Ph.D. thesis).
In this work we discuss the simplicial
program for topological field theories for the
case of nonabelian BF theory. Discrete BF
theory with finitedimensional space of fields
is constructed for a triangulated manifold (or
for a manifold equipped with a cubical cell
decomposition), that is in a sense equivalent to
the topological BF theory on the manifold. This
discrete version allows one to calculate certain
interesting quantities from the BF theory, like
the effective action on cohomology, in terms of
finitedimensional integrals instead of
functional integrals, as demonstrated in a
series of explicit examples. We also discuss the
interpretation of discrete BF action as the
generating function for the qLinfinity
structure (certain "oneloop version" of the
ordinary Linfinity algebra) on the cell
cochains of triangulation, related to the de
Rham algebra of the underlying manifold by the
homotopy transfer procedure. This work is a
refinement and buildup on our previous work
[arXiv:hepth/0610326].
 A. S. Cattaneo, P. Mnev, "Remarks
on ChernSimons invariants", Commun. Math. Phys.
293.3 (2010) 803836, arXiv:0811.2045
[math.QA].
The perturbative ChernSimons theory is studied in a
finitedimensional version or assuming that the propagator
satisfies certain properties (as is the case, e.g., with the
propagator defined by Axelrod and Singer). It turns out that
the effective BV action is a function on cohomology (with
shifted degrees) that solves the quantum master equation and
is defined modulo certain canonical transformations that can
be characterized completely. Out of it one obtains
invariants.
 F. Bonechi, P. Mnev, M.
Zabzine, "Finite
dimensional AKSZBV theories", Lett.
Math. Phys. 94.2 (2010) 197228, arXiv:0903.0995
[hepth].
We describe a canonical reduction of
AKSZBV theories to the cohomology of the source
manifold. We get a finite dimensional BV theory
that describes the contribution of the zero
modes to the full QFT. Integration can be
defined and correlators can be computed. As an
illustration of the general construction we
consider two dimensional Poisson sigma model and
three dimensional Courant sigma model. When the
source manifold is compact, the reduced theory
is a generalization of the AKSZ construction
where we take as source the cohomology ring. We
present the possible generalizations of the AKSZ
theory.
 A. Alekseev, P. Mnev, "Onedimensional
ChernSimons theory," Commun. Math. Phys.
307.1 (2011) 185227, arXiv:1005.2111
[hepth].
We study a onedimensional toy version of
the ChernSimons theory. We construct its
simplicial version which comprises features of a
lowenergy effective gauge theory and of a
topological quantum field theory in the sense of
Atiyah.
 A. S. Cattaneo, F.
Bonechi, P. Mnev, "The Poisson sigma model on closed
surfaces," JHEP 1 (2012), 127, arXiv:1110.4850
[hepth].
Using methods of formal geometry, the
Poisson sigma model on a closed surface is
studied in perturbation theory. The effective
action, as a function on vacua, is shown to have
no quantum corrections if the surface is a torus
or if the Poisson structure is regular and
unimodular (e.g., symplectic). In the case of a
Kahler structure or of a trivial Poisson
structure, the partition function on the torus
is shown to be the Euler characteristic of the
target; some evidence is given for this to
happen more generally. The methods of formal
geometry introduced in this paper might be
applicable to other sigma models, at least of
the AKSZ type.
 A. S. Cattaneo, P. Mnev,
N. Reshetikhin, "Classical
BV theories on manifolds with boundary,"
Commun. Math. Phys. 332.2 (2014) 535603, arXiv:1201.0290
[mathph].
In this paper we extend the classical BV
framework to gauge theories on spacetime
manifolds with boundary. In particular, we
connect the BV construction in the bulk with the
BFV construction on the boundary and we develop
its extension to strata of higher codimension in
the case of manifolds with corners. We present
several examples including electrodynamics,
YangMills theory and topological field theories
coming from the AKSZ construction, in
particular, the ChernSimons theory, the BF
theory, and the Poisson sigma model. This paper
is the first step towards developing the
perturbative quantization of such theories on
manifolds with boundary in a way consistent with
gluing.
 A. S. Cattaneo, P. Mnev,
N. Reshetikhin, "Classical and
quantum Lagrangian field theories with boundary,"arXiv:1207.0239
[mathph].
This note gives an introduction to
Lagrangian field theories in the presence of
boundaries. After an overview of the classical
aspects, the cohomological formalisms to resolve
singularities in the bulk and in the boundary
theories (the BV and the BFV formalisms,
respectively) are recalled. One of the goals
here (and in [arXiv:1201.0290]) is to show how
the latter two formalisms can be put together in
a consistent way, also in view of perturbative
quantization.
 P. Mnev, "A construction of
observables for AKSZ sigma models," Lett.
Math. Phys. 105.12 (2015) 17351783, arXiv:1212.5751
[mathph].
A construction of gaugeinvariant
observables is suggested for a class of
topological field theories, the AKSZ
sigmamodels. The observables are associated to
extensions of the target Qmanifold of the sigma
model to a Qbundle over it with additional
Hamiltonian structure in fibers.
 A. Alekseev, Y. Barmaz,
P. Mnev, "ChernSimons
theory with Wilson lines and boundary in the
BVBFV Formalism," J. Geom. and Phys. 67
(2013) 115, arXiv:1212.6256
[mathph].
We consider the ChernSimons theory with
Wilson lines in 3D and in 1D in the BVBFV
formalism of CattaneoMnevReshetikhin. In
particular, we allow for Wilson lines to end on
the boundary of the spacetime manifold. In the
toy model of 1D ChernSimons theory, the
quantized BFV boundary action coincides with the
Kostant cubic Dirac operator which plays an
important role in representation theory. In the
case of 3D ChernSimons theory, the boundary
action turns out to be the odd (degree 1)
version of the BF model with source terms for
the B field at the points where the Wilson lines
meet the boundary. The boundary space of states
arising as the cohomology of the quantized BFV
action coincides with the space of conformal
blocks of the corresponding WZW model.
 A. S. Cattaneo, P. Mnev,
"Wave relations,"
Commun. Math. Phys. 332.3 (2014) 10831111, arXiv:1308.5592
[mathph].
The wave equation (free boson) problem is
studied from the viewpoint of the relations on
the symplectic manifolds associated to the
boundary induced by solutions. Unexpectedly
there is still something to say on this simple,
wellstudied problem. In particular, boundaries
which do not allow for a meaningful Hamiltonian
evolution are not problematic from the viewpoint
of relations. In the twodimensional Minkowski
case, these relations are shown to be
Lagrangian. This result is then extended to a
wide class of metrics and is conjectured to be
true also in higher dimensions for nice enough
metrics. A counterexample where the relation is
not Lagrangian is provided by the Misner space.
 A. S. Cattaneo, P. Mnev,
N. Reshetikhin, "Semiclassical
quantization of classical field theories,"
Mathematical Aspects of Quantum Field Theories,
Springer (2015) 275324, arXiv:1311.2490
[mathph].
These lectures are an introduction to
formal semiclassical quantization of classical
field theory. First we develop the Hamiltonian
formalism for classical field theories on space
time with boundary. It does not have to be a
cylinder as in the usual Hamiltonian framework.
Then we outline formal semiclassical
quantization in the finite dimensional case.
Towards the end we give an example of such a
quantization in the case of Abelian ChernSimons
theory.
 P. Mnev, "Lecture notes on
torsions," arXiv:1406.3705
[math.AT].
These are the lecture notes for the
introductory course on Whitehead, Reidemeister
and RaySinger torsions, given by the author at
the University of Zurich in Spring semester
2014.
 A. S. Cattaneo, P. Mnev,
N. Reshetikhin, "Perturbative
quantum gauge theories on manifolds with
boundary," Commun. Math. Phys. 357.2
(2018) 631730, arXiv:1507.01221
[mathph].
This paper
introduces a general perturbative quantization
scheme for gauge theories on manifolds with
boundary, compatible with cutting and gluing, in
the cohomological symplectic (BVBFV) formalism.
Explicit examples, like abelian BF theory and
its perturbations, including nontopological
ones, are presented.
 A. Alekseev, O.
Chekeres, P. Mnev, "Wilson surface observables from
equivariant cohomology," JHEP 93.11
(2015), arXiv:1507.06343
[hepth].
Wilson lines in gauge theories admit
several path integral descriptions. The first
one (due to AlekseevFaddeevShatashvili) uses
path integrals over coadjoint orbits. The second
one (due to DiakonovPetrov) replaces a
1dimensional path integral with a 2dimensional
topological σmodel. We show that this σmodel
is defined by the equivariant extension of the
Kirillov symplectic form on the coadjoint orbit.
This allows to define the corresponding
observable on arbitrary 2dimensional surfaces,
including closed surfaces. We give a new path
integral presentation of Wilson lines in terms
of Poisson σmodels, and we test this
presentation in the framework of the
2dimensional YangMills theory. On a closed
surface, our Wilson surface observable turns out
to be nontrivial for G nonsimply connected (and
trivial for G simply connected), in particular
we study in detail the cases G=U(1) and G=SO(3).
 A. S. Cattaneo, P. Mnev,
K. Wernli, "Split
ChernSimons theory in the BVBFV formalism,"
Quantization, Geometry and
Noncommutative Structures in Mathematics
and Physics, Springer, Cham (2017)
293324, arXiv:1512.00588
[math.GT].
The goal of this note is to give a brief
overview of the BVBFV formalism developed by
the first two authors and Reshetikhin in
[arXiv:1201.0290], [arXiv:1507.01221] in order
to perform perturbative quantisation of
Lagrangian field theories on manifolds with
boundary, and present a special case of
ChernSimons theory as a new example.
 A. S. Cattaneo, P. Mnev,
N. Reshetikhin, "Perturbative BV
theories with Segallike gluing," arXiv:1602.00741
[mathph].
This is a survey of our program of
perturbative quantization of gauge theories on
manifolds with boundary compatible with
cutting/pasting and with gauge symmetry treated
by means of a cohomological resolution
(BatalinVilkovisky) formalism. We also give two
explicit quantum examples  abelian BF theory
and the Poisson sigma model. This exposition is
based on a talk by P.M. at the ICMP 2015 in
Santiago de Chile.
 A. S. Cattaneo, P. Mnev,
N. Reshetikhin, "A cellular
topological field theory," Commun.
Math. Phys. 374 (2020), 12291320,
arXiv:1701.05874
[math.AT].
We present a construction of cellular BF theory (in
both abelian and nonabelian variants) on cobordisms
equipped with cellular decompositions. Partition functions
of this theory are invariant under subdivisions, satisfy a
version of the quantum master equation, and satisfy
AtiyahSegaltype gluing formula with respect to composition
of cobordisms.
 P.
Mnev, "Lectures
on BatalinVilkovisky formalism and its
applications in topological quantum field
theory,"
arXiv:1707.08096
[mathph].
Lecture notes for the course "BatalinVilkovisky
formalism and applications in topological quantum field
theory" given at the University of Notre Dame in the Fall
2016 for a mathematical audience. In these lectures we give
a slow introduction to the perturbative path integral for
gauge theories in BatalinVilkovisky formalism and the
associated mathematical concepts.
 A. S. Losev, P. Mnev, D.
R. Youmans, "Twodimensional
abelian BF theory in Lorenz gauge as a twisted N=(2,2)
superconformal field theory," J.
Geom. Phys. 131C (2018) 122137, arXiv:1712.01186
[hepth].
We study the twodimensional topological abelian BF theory
in the Lorenz gauge and, surprisingly, we find that the
gaugedfixed theory is a free type B twisted N = (2, 2)
superconformal theory with odd linear target space, with the
ghost field c being the pullback of the linear holomorphic
coordinate on the target. The BRST charge of the gaugefixed
theory equals the total Q of type B twisted theory. This
unexpected identification of two different theories opens a
way for nontrivial deformations of both of these theories.
 A.
S. Cattaneo, P. Mnev, N. Reshetikhin, "Poisson sigma model
and semiclassical quantization of integrable
systems," in Ludwig Faddeev
Memorial Volume: A Life in Mathematical Physics,
World Scientific (2018), arXiv:1803.07723
[mathph].
In this paper we outline the construction
of semiclassical eigenfunctions of integrable
models in terms of the semiclassical path
integral for the Poisson sigma model with the
target space being the phase space of the
integrable system. The semiclassical path
integral is defined as a formal power series
with coefficients being Feynman diagrams. We
also argue that in a similar way one can obtain
irreducible semiclassical representations of
Kontsevich's star product.
 R.
Iraso, P. Mnev, "Twodimensional
YangMills theory on surfaces with corners in
BatalinVilkovisky formalism," Commun.
Math. Phys. 370.2 (2019) 637702, arXiv:1806.04172
[mathph].
In this paper we recover the
nonperturbative partition function of 2D
YangMills theory from the perturbative path
integral. To achieve this goal, we study the
perturbative path integral quantization for 2D
YangMills theory on surfaces with boundaries
and corners in the BatalinVilkovisky formalism
(or, more precisely, in its adaptation to the
setting with boundaries, compatible with gluing
and cutting  the BVBFV formalism). We prove
that cutting a surface (e.g. a closed one) into
simple enough pieces  building blocks  and
choosing a convenient gaugefixing on the
pieces, and assembling back the partition
function on the surface, one recovers the known
nonperturbative answers for 2D YangMills
theory.
 A.
S. Cattaneo, P. Mnev, K. Wernli, "Theta Invariants of
lens spaces via the BVBFV formalism,"
arXiv:1810.06663
[math.AT].
The goal of this paper is to investigate
the Theta invariant  an invariant of framed 3
manifolds associated with the lowest order
contribution to the ChernSimons partition
function  in the context of the quantum BVBFV
formalism. Namely, we compute the state on the
solid torus to low degree in , and apply the
gluing procedure to compute the Theta invariant
of lens spaces. We use a distributional
propagator which does not extend to a
compactified configuration space, so to compute
loop diagrams we have to define a regularization
of the product of the distributional
propagators, which is done in an ad hoc fashion.
Also, a polarization has to be chosen for the
quantization process. Our results agree with
results in the literature for one type of
polarization, but for another type of
polarization there are extra terms.
 A.
S. Losev, P. Mnev, D. R. Youmans, "Twodimensional nonabelian
BF theory in Lorenz gauge as a solvable logarithmic
TCFT," Commun. Math.
Phys. (2019), arXiv:1902.02738
[hepth].
We study twodimensional nonabelian BF theory in Lorenz
gauge and prove that it is a topological conformal field
theory. This opens the possibility to compute topological
string amplitudes (GromovWitten invariants). We found that
the theory is exactly solvable in the sense that all
correlators are given by finitedimensional convergent
integrals. Surprisingly, this theory turns out to be
logarithmic in the sense that there are correlators given by
polylogarithms and powers of logarithms. Furthermore, we
found fields with "logarithmic conformal dimension"
(elements of a Jordan cell for L_0). We also found certain
vertex operators with anomalous dimensions that depend on
the nonabelian coupling constant. The shift of dimension of
composite fields may be understood as arising from the
dependence of subtracted singular terms on local
coordinates. This generalizes the wellknown explanation of
anomalous dimensions of vertex operators in the free scalar
field theory.
 P.
Mnev, M. Schiavina, K. Wernli, "Towards holography in the BVBFV setting,"
Annales Henri Poincare 21 (3), 9931044,
arXiv:1905.00952
[mathph].
We show how the BVBFV formalism provides natural solutions
to Witten descent equations, and discuss how it relates to
the emergence of holographic counterparts of given gauge
theories. Furthermore, by means of an AKSZtype construction
we reproduce the ChernSimons to WessZuminoWitten
correspondence from infinitesimal local data, and show an
analogous correspondence for BF theory. We discuss how
holographic correspondences relate to choices of
polarisation relevant for quantisation, proposing a
semiclassical interpretation of the quantum holographic
principle.
 S.
Kandel, P. Mnev, K. Wernli, "Twodimensional perturbative
scalar QFT and AtiyahSegal gluing," arXiv:1912.11202
[mathph].
We
study the perturbative quantization of 2dimensional
massive scalar field theory with polynomial (or
power series) potential on manifolds with boundary.
We prove that it fits into the functorial quantum
field theory framework of AtiyahSegal. In
particular, we prove that the perturbative partition
function defined in terms of integrals over
configuration spaces of points on the surface
satisfies an AtiyahSegal type gluing formula.
Tadpoles (short loops) behave nontrivially under
gluing and play a crucial role in the result.
 A.
S. Cattaneo, P. Mnev, K. Wernli, "Constrained systems,
generalized HamiltonJacobi actions, and quantization," arXiv:2012.13270
[mathph].
Mechanical systems(i.e., onedimensional field
theories)with constraints are the focus of this paper. In
the classical theory, systems with infinitedimensional
targets are considered as well (this then encompasses also
higherdimensional field theories in the hamiltonian
formalism). The properties of the HamiltonJacobi (HJ)
action are described in details and several examples are
explicitly computed (including nonabelian ChernSimons
theory, where the HJ action turns out to be the gauged
WessZuminoWitten action). Perturbative quantization,
limited in this note to finitedimensional targets, is
performed in the framework of the BatalinVilkovisky (BV)
formalism in the bulk and of the BatalinFradkinVilkovisky
(BFV) formalism at the endpoints. As a sanity check of the
method, it is proved that the semiclassical contribution of
the physical part of the evolution operator is still given
by the HJ action. Several examples are computed explicitly.
In particular, it is shown that the toy model for nonabelian
ChernSimons theory and the toy model for 7D ChernSimons
theory with nonlinear Hitchin polarization do not have
quantum corrections in the physical part (the extension of
these results to the actual cases is discussed in the
companion paper). Background material for both the classical
part (symplectic geometry, generalized generating functions,
HJ actions, and the extension of these concepts to
infinitedimensional manifolds) and the quantum part (BVBFV
formalism) is provided.

A. S. Cattaneo, P. Mnev, K. Wernli, "
Quantum
ChernSimons theories on cylinders: BVBFV partition
functions,"
arXiv:2012.13983
[hepth].
We compute partition functions of
ChernSimons type theories for cylindrical spacetimes I x
Σ, with I an interval and dim Σ = 4l + 2, in the BVBFV
formalism (a refinement of the BatalinVilkovisky
formalism adapted to manifolds with boundary and
cuttinggluing). The case dim Σ = 0 is considered as a toy
example. We show that one can identify  for certain
choices of residual fields  the "physical part"
(restriction to degree zero fields) of the BVBFV
effective action with the HamiltonJacobi action computed
in the companion paper, without any quantum corrections.
This HamiltonJacobi action is the action functional of a
conformal field theory on Σ. For dim Σ = 2, this implies a
version of the CSWZW correspondence. For dim Σ = 6, using
a particular polarization on one end of the cylinder, the
ChernSimons partition function is related to
KodairaSpencer gravity (a.k.a. BCOV theory); this
provides a BVBFV quantum perspective on the semiclassical
result by Gerasimov and Shatashvili.
Book:
P. Mnev, "
Quantum Field Theory:
BatalinVilkovisky Formalism and Its Applications," AMS
University Lecture Series 72 (2019).
Link to the book
webpage on the publisher's website.
This book originated from lecture notes for the course
given by the author at the University of Notre Dame in the fall
of 2016. The aim of the book is to give an introduction to the
perturbative path integral for gauge theories (in particular,
topological field theories) in BatalinVilkovisky formalism and
to some of its applications. The book is oriented toward a
graduate mathematical audience and does not require any prior
physics background. To elucidate the picture, the exposition is
mostly focused on finitedimensional models for gauge systems
and path integrals, while giving comments on what has to be
amended in the infinitedimensional case relevant to local field
theory. Motivating examples discussed in the book include
AlexandrovKontsevichSchwarzZaboronsky sigma models, the
perturbative expansion for ChernSimons invariants of
3manifolds given in terms of integrals over configurations of
points on the manifold, the BF theory on cellular decompositions
of manifolds, and Kontsevich's deformation quantization formula.
Some talk slides and
recordings:
 Talk "Twodimensional perturbative
scalar field theory with polynomial potential and
cuttinggluing" (at Zoom
Seminar: Differential Geometry and Mathematical Physics,
6/12/2020): video
recording, slides.
 Talk "Twodimensional BF theory as a
conformal field theory" Simons Center workshop
5/21/2019:
video recording; EIMI St. Petersburg (Faddeev'85
conference) 05/27/2019: slides.
 Talk "2D YangMills theory on surfaces with corners in BV
formalism" (UC Davis, 05/25/2018): notes.
 Talk "Cellular BVBFVBF theory" (at the workshop
"Field theories and higher structures in mathematics and
physics", BIRS Oaxaca, 06/49/2017):
video
recording.
 Talk "Around AKSZ sigma models" ("Gone Fishing"
Poisson geometry conference, Notre Dame, 05/04/2017): notes.
 Seminar talk "Torsion as an integral"
(Poncelet Laboratory, Moscow, 04/19/2017): notes.
 Talk at the Poisson
2016 conference "BF
theory on cobordisms endowed with cellular decomposition"
(ETH Zurich, 07/04/2016): slides, video
recording.
 Habilitation talk "BV pushforwards and exact
discretizations in topological field theory" (University
of Zurich, 02/29/2016): slides.
 Colloquium talk "Quantum BV theories on manifolds with boundary"
(University of Notre Dame, 10/28/2015): slides.
 Talk at the International
Congress in Mathematical Physics 2015 "Perturbative topological
field theory with Segallike gluing" (Santiago de
Chile, 07/27/2015): slides.
 Talk "An
example of a cellular topological quantum field theory
in BVBFV formalism, with Segallike gluing" (at
Simons Center for Geometry and Physics workshop "Homological
methods in quantum field theory", 09/2910/03/2014):
video
recording.
 Talk "Towards
perturbative topological field theory on manifolds with
boundary" (QGM Aarhus, 03/12/2013): slides.
 Talk "Hidden
algebraic structure on cohomology of simplicial
complexes, and TFT" (Trinity College Dublin,
02/04/2013): slides.
Expository material:
 Quantum mechanics on
graphs (a contribution to MPIM Jahrbuch 2016): here
(in German; translation by Christian Kaiser). Here is the draft in English.
 Perturbative topological
quantum field theory on manifolds with boundary  a
poster for Panorama
of Mathematics event in Hausdorff Center for
Mathematics, Bonn (10/2123/2015). Here.
Teaching:
Fall 2021: MATH 70330
Intermediate Geometry
and Topology.
Link to
the course webpage.
Spring 2021: MATH
2058005, 2058006
Introduction
to linear algebra and differential equations.
Course
website:
link.
Fall 2020: MATH
60330 Basic Geometry and Topology.
Link to the course webpage.
Spring 2020: MATH
2058005, 2058006 Introduction
to linear algebra and differential equations.
Link
to the course webpage.
Notes.
Fall 2019: MATH 70330
Intermediate Geometry
and Topology.
A
Kan style graduate student seminar. Link to the course webpage.
Spring 2019: MATH
80440 Topics in topology II: "Introduction to conformal
field theory."
Here are the syllabus
and course plan.
Notes: 1/162/22, 2/253/25, 3/274/8, 4/105/1. Exercises: 2/1, 2/8, 2/15, 3/1, 3/8, 3/29, 4/5, 4/26.
Fall 2018: MATH
2055004, 2055006 Calculus
III.
Link
to the course webpage. Notes:
8/22,
8/24,
8/27,
8/29,
8/31,
9/3,
9/5,
9/7,
9/10,
9/12,
9/14,
9/19,
9/21,
9/24,
9/28,
10/1,
10/3,
10/5,
10/8,
10/10,
10/12,
10/22,
10/26,
10/29,
10/31,
11/2,
11/5,
11/7,
11/9,
11/12,
11/16,
11/19,
11/28,
11/30,
12/3.
Spring 2018: MATH
2058003, 2058005 Introduction
to linear algebra and differential equations.
Link
to the course webpage. Notes:
1/17,
1/19,
1/24,
1/26,
1/29,
1/31,
2/2,
2/5,
2/7,
2/9,
2/12,
2/14,
2/16,
2/19,
2/21,
2/23,
2/26,
2/28,
3/2,
3/5,
3/7,
3/9,
3/19,
3/21,
3/23,
3/26,
3/28,
4/4,
4/6,
4/9,
4/11,
4/13,
4/16,
4/18,
4/20,
4/23,
4/25,
4/27,
4/30,
5/2.
Fall
2017: MATH 70330 Intermediate Geometry and Topology.
A
Kan style graduate student seminar. Here are the syllabus and the detailed plan.
Spring 2017:
MATH 2058004 Introduction
to linear algebra and differential equations.
Link to the
course webpage.
Fall 2016:
MATH 80430 Topics in topology I: "BatalinVilkovisky formalism and applications
in topological quantum field theory."
Link to the course
webpage.
Some
materials from courses and minicourses I have taught
in the past:
Quantum BV
theories on manifolds with boundary (a
minicourse at the conference Higher
Structures in Geometry and Physics 2015, MPIM
Bonn, October 2015).
Notes: part 1, part 2.
Introduction
to quantum electrodynamics for mathematicians
(a minicourse at MPIM Bonn, December 2014).
Notes: 1 2.
BatalinVilkovisky
formalism in topological quantum field theory
(MPIM Bonn/University of Bonn, Fall 2014).
Program: here.
Notes: part 1, part 2, part 3.
Torsions
(University of Zurich, Spring 2014).
Poster: here.
Notes: arXiv:1406.3705
[math.AT].
Moduli space of flat
connections (a minicourse at the Galileo Galilei
Insitute, Florence, October 2013).
Video recording of the lectures: 1
2
3.
Notes (in Russian!) from another instance of this
minicourse (Chebyshev Laboratory, St. Petersburg, May
2013): 13.
Topological quantum
field theory (University of Zurich, Spring 2013).
Notes: here.
Conformal field theory,
part II (University
of Zurich, Fall 2011).
Notes: 2 3 4,5 6 7,8 9 10 11 12 13 14.
Course webpage: link.
Conformal field theory,
part I (University of Zurich, Spring 2011).
Notes: 1 2 3 4 5 6 7 8 9 10 11 12 13 14.
Course webpage: link.
Also:
My father is a mathematician: webpage.
Link to my
old webpage.
Also, I like to play Irish
and Breton
music on flute.