Associate
Professor of Machine Learning, RPL, EECS, KTH

Welcome

My current research focuses on two main directions: 1) machine
learning algorithms with a geometric or topological flavour or which utilize
insights about geometry in the context of other methods such as deep learning and 2) machine
learning methods that are tailored for robotic manipulation or motion planning
and which incorporate available domain knowledge and information
about physics and configuration space geometry in order to be data efficient.

Short Biography

I am currently an Associate Professor of Machine Learning within the division
of Robotics, Perception and Learning at KTH Royal Institute of Technology.
During 05/2015-04/2016, I was conducting post-doctoral research as a visiting J-1 research scholar/visiting assistant project
scientist with the AMPlab and the Berkeley
Automation Science Lab at the University of California, Berkeley where I
worked under supervision of Prof. Ken Goldberg. Previously, I was fortunate to
be a researcher and postdoc working with Prof. Danica Kragic and her group.
Before then, I was a pure mathematician and completed my PhD entitled "The
Bergman Kernel on Toric Kähler Manifolds" under supervision of Prof. Michael
Singer at the University of Edinburgh. Before that, I received my BSc
mathematics from the University of Edinburgh and a Master of Advanced Study in
Mathematics (Part III) from the University of Cambridge and also spent a year
as an exchange student at the National University of Singapore.

Co-organizing ICRA 2021 workshop Bridging the Gap between Data-driven and Analytical Physics-based Grasping and Manipulation II
with Yasemin Bekiroglu, Naresh Marturi, Marc Peter Deisenroth, Yiannis Karayiannidis, Miao Li, Robert Platt.

Co-organizing ICRA 2021 workshop "Representing and Manipulating Deformable Objects" with
Anastasiia Varava, Martina Lippi, Michael C. Welle, Hang Yin, Rika Antonova, Danica Kragic, Yiannis Karayiannidis, Ville Kyrki, Alessandro Marino, Júlia Borràs, Guillem Alenyà, Carme Torras

PhD course on Topological
Data Analysis for WASP students to be taught again in
2021 with Martina Scolamiero and Wojciech Chacholsky

Andrea
Baisero, Master Degree Project 2012,Swedish AI Society's best master thesis award,
supervision with C. H. Ek and D. Kragic
Thesis: "Encoding
Sequential Structures using Kernels", next: PhD student University of Stuttgart and Northeastern University

Master Degree Projects

If you are interested in any of the topics below or would like to suggest your own topic,
drop me an email with your CV and transcripts attached as well as a reason for why you are
interested in this topic. Please note that I only have capacity to consider
students that are already registered at KTH for thesis project work.

Multiple topics in anomaly detection for financial transaction data,
in collaboration with Salla Franzén, Chief Data Scientist, SEB.

Topological Data Analysis at Scale. This project will investigate
to what extent recently developed techniques in Topological Data Analysis
can be used for the classification of images.

The geometric properties of Deep Learning. This project will utilize
our recent work on high dimensional Voronoi Cell decompositions and
Montecarlo Ray casting to explore geometric properties of Deep Neural
Networks.

Robotic manipulation at Scale. Iterative miniature robotic arm design using 3D printing and rapid prototyping.

Dex-Net 1.0: A Cloud-Based Network of 3D Objects and a
Multi-Armed Bandit Model with Correlated Rewards to Accelerate
Robust Grasp Planning

Jeffrey Mahler, Florian T. Pokorny, Brian Hou, Melrose
Roderick, Michael Laskey, Mathieu Aubry, Kai Kohlhoff, Torsten
Kroeger, James Kuffner, Ken Goldberg

IEEE ICRA, 2016, Finalist, Best Manipulation Paper Award, ICRA 2016

Let $(L,h)\to (X, \omega)$ be a compact toric polarized Kähler manifold of
complex dimension $n$. For each $k\in \mathbb{N}$, the fibre-wise Hermitian metric
$h^k$ on $L^k$ induces a natural inner product on the vector space $\mathcal{C}^{\infty}(X,
L^k)$ of smooth global sections of $L^k$ by integration with respect to the
volume form $\frac{\omega^n}{n!}$. The orthogonal projection
$P_k:\mathcal{C}^{\infty}(X, L^k)\to H^0(X, L^k)$ onto the space $H^0(X, L^k)$ of global
holomorphic sections of $L^k$ is represented by an integral kernel $B_k$ which
is called the Bergman kernel (with parameter $k\in \mathbb{N}$). The restriction $\rho_k:X\to
\mathbb{R}$ of the norm of $B_k$ to the diagonal in $X\times X$ is called the density
function of $B_k$.
On a dense subset of $X$, we describe a method for computing the coefficients of
the asymptotic expansion of $\rho_k$ as $k\to \infty$ in this toric
setting. We also provide a direct proof of a result which illuminates the
off-diagonal decay behaviour of toric Bergman kernels.
We fix a parameter $l\in \mathbb{N}$ and consider the projection $P_{l,k}$ from
$\mathcal{C}^{\infty}(X, L^k)$ onto those global holomorphic sections of $L^k$ that
vanish to order at least $lk$ along some toric submanifold of $X$. There exists an
associated toric partial Bergman kernel $B_{l, k}$ giving rise to a toric partial density function
$\rho_{l, k}:X\to \mathbb{R}$.
For such toric partial density functions,
we determine new asymptotic expansions over
certain subsets of $X$ as $k\to \infty$. Euler-Maclaurin sums and Laplace's method are utilized as important
tools for this. We discuss the case of a polarization of $\mathbb{CP}^n$ in detail
and also investigate the non-compact Bargmann-Fock model with imposed vanishing
at the origin.
We then discuss the relationship between the slope inequality and the asymptotics
of Bergman kernels with vanishing and study how a version of Song and Zelditch's
toric localization of sums result generalizes to arbitrary polarized Kähler
manifolds.
Finally, we construct families of induced metrics on blow-ups of
polarized Kähler manifolds. We relate those metrics to partial density
functions and study their properties for a specific blow-up of $\mathbb{C}^n$ and $\mathbb{CP}^n$
in more detail.

@phdthesis{pokorny2011a,
title = {The Bergman Kernel on Toric K{\"a}hler Manifolds},
author = {Pokorny, Florian T.},
year = {2011},
school = {The University of Edinburgh},
doi = {1842/5301},
url = {http://www.csc.kth.se/~fpokorny/static/publications/FTPokornyPhD.pdf},
}