REMOLD

The REMOLD doctoral network kicked off the academic year with an
opening school, which was a fantastic opportunity for the REMOLD
students to get to know each other in person, as well as to learn some
foundational topics related to their PhD. The opening school took
place in Essen and was organised by Remold PI, Victoria Hoskins, and
was also partially supported by the RTG 2553. The school featured four
lecture courses by Pramod Achar, Simon Pepin Lehalleur, Simon Riche
and Remold PI, Olivier Taïbi, as well as two special talks by REMOLD
PIs, Jens Eberhardt and Jakob Scholbach. The school was advertised
beyond the REMOLD network, and approximately 50 people attended.

The school started with a team building event for the REMOLD students
led by Chiat Cheong, which focused on finding common interests and
getting to know each other. One of the main activities was for the
students to plan an outreach event together, which we hope the
students may get to put into practice later on. From the REMOLD
students’ feedback, Antoine said “I really learned some things about
the other students’ personalities and it sparked some nice
conversations later on” and Thomas found Chiat “thoughtful and clearly
passionate about her work.” Leonardo added that “The team building day
was so effective that for the whole week we struggled to arrive at the
lectures on time in the morning, because we stayed up until late to
spend time together. I would call that a success”.

Simon Riche opened the school with his lecture course on the
representation theory of reductive algebraic groups, which was a
whistle-stop-tour of some of the essential background in
representation theory that is a common theme in all PhD topics of the
REMOLD students. Michał said this was his favourite course, as “it
struck the right balance in terms of the amount of detail to provide for the time available” and Andrea “especially appreciated how
the interplay between geometry and representation theory was
showcased”. Antoine really enjoyed “the last lecture focusing on
positive characteristic phenomena.”

Simon Riche’s course on the
representation theory of reductive algebraic groups

Simon Pepin Lehalleur’s course on motivic sheaves was also essential
foundational material for many of the REMOLD students. Leonardo said
“The course I enjoyed the most is Simon’s course on motivic sheaves,
as it covered many topics that I need to study for my project, and I
was able to keep up with it.” Zhen added that Simon’s course “helped me unravel some of the ‘black boxes’ in my project and better
understand the history behind the subject—how the ideas were motivated
and how they were eventually achieved.”

Simon Pepin Lehalleur’s course on motivic sheaves

Olivier Taïbi’s course on Shimura varieties was the closest the school
came to touching on the ‘Langlands’ aspect of the REMOLD network, and
Olivier started with a very geometric introduction to motivate his course. Thomas said this was his favourite course as it “helped me
place many things that I had previously learned into a broader
perspective. It was both motivating and enlightening — particularly the final lecture, where open questions were discussed!”

Olivier Taïbi’s course on Shimura varieties

Pramod Achar’s lecture course on infinity categories received lots of
praise due to his charismatic lecturing style. Zhen said Pramod
“presented each topic in a thoughtful way, offering plenty of
intuition about what is really going on.” He added that “The exercise
sessions were also a great opportunity to get my hands dirty with
concrete fun examples.” Vukašin was “enthralled by the lecturing
of Prof. Achar” and Ilan said Pramod made delving into the foundations
of infinity categories “surprisingly engaging”. Leonardo added: “Even
though I was already familiar with the content, It was a real
pleasure to listen to his lectures.”

Pramod Achar’s course on infinity categories

There were two special talks given by Remold PIs, which in the words
of Ilan “both had awesome energy”. Jakob Scholbach gave a lecture on
dualizability, which Antoine said was his favourite lecture, as “it
really highlighted for me how deep the existence of this formalism of
duality is, and helped motivate the course on motivic sheaves”. Jens
Eberhardt gave a lecture on gluing together representations and flag
varieties, which was mentioned as a highlight of the week by Michał
because “it was nice to see some hands-on geometry being done” and by
Zhen as it “offered an inspiring perspective” and “helped me take a
step forward in my own work.” Indeed, Vukašin echoed these sentiments:
“The highlight of the school for me were the two lectures given by
Prof. Eberhardt and Prof. Scholbach, as they were able to motivate the
theory that we were studying through some classical examples.”

Jens
Eberhardt’s lecture on gluing together representations and flag
varieties

Overall the school was very successful in its aims: the speakers
created a warm and inviting atmosphere that fostered lively
discussions and interactions, and the REMOLD students learned a lot of
important foundational mathematics which will stand them in good stead
for starting research on their individual projects. We conclude with
some words from Leonardo that sum up the school: “The highlight for me
is how much was achieved in a single week: plenty of interesting
lectures, and of interesting conversations in between these lectures,
and the plenty of new people I met, especially the other REMOLD students.”

The atmosphere at the Lecture Room of the school at the University of Duisburg-Essen