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Teaching


I have taught/tutored the following courses at the Humboldt-Universität zu Berlin :-


Sommersemester 2022       Topics Course - An introduction to the Ricci Flow (Instructor).


Wintersemester 2022        Topology Ⅱ & Differential Geometry Ⅰ (both tutored).


Sommersemester 2021       Topology Ⅰ (Instructor).


Wintersemester 2020-21      Funktionalanalysis (tutor. The instructor is Prof. Chris Wendl).


I have taught the following courses at the University of Waterloo :-


Fall 2019            MATH 124 - Calculus and Vector Algebra for Kinesiology.


Fall 2018            PMATH 336 - Introduction to Group Theory and its Applications.


Student advising

Anton Iliashenko (NSERC-Undergraduate Student Research Assistant) Spring 2019. (co-supervised with Spiro Karigiannis)

Project title: "Flows of metrics induced from mean curvature flow"

Project abstract: The mean curvature flow is a flow of an isometrically immersed submanifold M inside an ambient Riemannian manifold X in the direction of the mean curvature vector field. The Ricci flow is an i ntrinsic flow of a metric on a Riemannian manifold M in the direction of (minus) the Ricci tensor. Let M be a Riemannian manifold and consider it as the zero section inside one of its tensor bundles X, such as the cotangent bundle X = T* M or the real canonical bundle X = Λn (T* M) where n = dim(M). Using the Levi-Civita connection of M, there is a canonical Riemannian metric induced on X, which makes the zero section isometrically immersed. Therefore one can evolve M inside X by the mean curvature flow. For small time, this evolution Mt will be canonically diffeomorphic to M using the exponential map on the mean curvature vector field. Pulling back via this diffeomorphism, the mean curvature flow of M in X thus induces an intrinsic flow of metrics on M.

The natural question is: what is this induced flow of metrics? If it is the Ricci flow, this gives a new interesting characterization of Ricci flow. If it is not the Ricci flow, this could be a new interesting canonical flow of metrics. Moreover, in the case when X = T* M, the zero section is Lagrangian, and mean curvature flow preserves the Lagrangian condition. The Lagrangian mean curvature flow is well-behaved. Similarly, when X = Λn (T* M), then M is a hypersurface in X. The hypersurface mean curvature flow is also well-behaved.


I have been a TA (duties include : taking tutorial sessions, marking assignments and exam papers, holding office hours and occasionally teaching a class) for the following courses at the University of Waterloo :-


Spring 2019           PMATH 321 - Non-Euclidean geometry

Winter 2019            PMATH 467/667 - Algebraic Topology

                  MATH 135 - Algebra for Honours

Spring 2018           PMATH 347 - Groups and Rings

Winter 2018           PMATH 365 - Elementary Differential Geometry

                  MATH 148 - Advanced Calculus

Fall 2017                MMT 640 - An Introduction to Algebraic Number Theory (online)

Spring 2017           MMT 648 - Calculus for Teachers (online)

Winter 2017           PMATH 467/667 - Algebraic Topology

Fall 2016              MATH 135 - Algebra for Honours

                  MATH 115 - Linear Algebra for Beginners

Winter 2016           PMATH 365- Elementary Differential Geometry

Spring 2016           MMT 636 - Linear Algebra for Teachers (online)

Fall 2015              PMATH 465/665 - Geometry of Manifolds

                  MATH 127 - Calculus for Sciences