Photo by Doktent  Own work, CC BYSA 4.0, clipped

SFB student workshop 9–13 August 2021 + research conference 13–15 August 2021
Perspectives on quantum link homology theories
Please note that this is a past event.





We are organizing a student workshop based around recent developments in link homology theories, with particular focus on Khovanov homology and other quantum homology theories. The workshop will be paired with and provide background for a twoday research conference.
poster
health and safety measures

venue Faculty of Mathematics, University of Regensburg/online

workshop lecturers

special lecturer

conference speakers

Akram Alishahi, University of Georgia, Athens

Cristina Anghel, University of Oxford

Artem Kotelskiy, University of Indiana, Bloomington

Marco Marengon, Max Planck Institute for Mathematics, Bonn

Krzysztof Putyra, University of Zurich

Hoel Queffelec, Institut Montpelliérain Alexander Grothendieck

Liam Watson, University of British Columbia

organizers
If you have any questions or concerns about the event, please contact the organizers at
lukas@DELETEME@lewark.de or
claudius.zibrowius@DELETEME@posteo.net.
This event is funded by the SFB 1085 Higher Invariants.
The svgicons on this website are taken from mailpile; they are free to use under the GNU Affero General Public License.
To view the abstract of a lecture or talk, please click on its title. There, you will also find links to the individual recordings and lecture notes/slides (if available).
Our video channel on the university media library
before the workshop 
 Andrew Lobb\(^\dagger\) 
lecture 1: Spectral Sequences and Khovanov homology
lecture notes
video
We give the construction of the most vanilla flavor of Khovanov homology.

Monday 
15.30
 LouisHadrien Robert 
lecture 1: gl(N) link homology via foams
lecture notes (all in one)
video
I'll give a definition of colored gl(N) quantum link
invariants using graph colorings and sketch a proof of invariance. I'll
use an interpretation of quantum binomials as graded cardinals.

17.00
 Melissa Zhang* 
lecture 1: A perspective on annular Khovanov homology
lecture notes
video
A link \(L\) living in a thickened annulus \((\mathbb{R}^2 \smallsetminus \{0\})\times[0,1]\) is called an annular link. The ambient space equips the bigraded Khovanov chain complex of \(L\) with an additional annular (filtration) grading, and the associated graded complex computes the annular Khovanov homology, AKh(\(L\)). Understanding annular knots and links is important in many different contexts in lowdimensional topology; this lecture series will survey some existing and potential relationships between AKh and contact topology, knot concordance, representation theory, and more.
Some familiarity with Khovanov homology at the level of Dror BarNatan's introductory paper on Khovanov homology is recommended. Fun computational exercises will be provided.

Tuesday 
10.30
 Andrew Lobb\(^\dagger\) 
lecture 2: Spectral Sequences and Khovanov homology
lecture notes
video
We discuss homology and spectral sequences in general, and see how to understand them through Gauss elimination.

11.30
 Q&A session zoom

13.30
 Paul Wedrich 
lecture 1: Invariants of 4manifolds from KhovanovRozansky link homology
video
Ribbon categories are 3dimensional algebraic structures that control quantum link polynomials and that give rise to 3manifold invariants known as skein modules. I will describe how to use KhovanovRozansky link homology, a categorification of the gl(N) quantum link polynomial, to obtain a 4dimensional algebraic structure that gives rise to vector spacevalued invariants of smooth 4manifolds, following this paper with Scott Morrison and Kevin Walker.
Lecture 1 will be on 'KhovanovRozansky gl(N) link homology: introduction, functoriality'.
For lecture notes, please contact Paul directly via email.

14.30
 Q&A session discord/exercise session

15.45
 LouisHadrien Robert 
lecture 2: gl(N) link homology via foams
lecture notes (all in one)
video
Combinatorial ideas of Lecture 1 are upgraded to a 2
dimensional setting: We will consider foams instead of graphs. I'll give
foam evaluation formulas and show that they satisfy some local
relations.

17.00
 Melissa Zhang* 
lecture 2: A perspective on annular Khovanov homology
lecture notes
video
A link \(L\) living in a thickened annulus \((\mathbb{R}^2 \smallsetminus \{0\})\times[0,1]\) is called an annular link. The ambient space equips the bigraded Khovanov chain complex of \(L\) with an additional annular (filtration) grading, and the associated graded complex computes the annular Khovanov homology, AKh(\(L\)). Understanding annular knots and links is important in many different contexts in lowdimensional topology; this lecture series will survey some existing and potential relationships between AKh and contact topology, knot concordance, representation theory, and more.
Some familiarity with Khovanov homology at the level of Dror BarNatan's introductory paper on Khovanov homology is recommended. Fun computational exercises will be provided.

Wednesday 
10.30
 Andrew Lobb\(^\dagger\) 
lecture 3: Spectral Sequences and Khovanov homology
lecture notes
video
We talk through the construction of Lee homology and talk briefly about some other spectral sequences.

11.30
 Q&A session zoom

13.30
 Paul Wedrich 
lecture 2: Invariants of 4manifolds from KhovanovRozansky link homology
video
Lecture 2 will be about 'KhovanovRozansky gl(N) link homology: properties, diagram independence'.
For lecture notes, please contact Paul directly via email.

14.30
 Q&A session discord/exercise session

15.45
 LouisHadrien Robert 
lecture 3: gl(N) link homology via foams
lecture notes (all in one)
video
I'll explain how to derive functors from foam evaluations and
how to use it to construct colored gl(N) link homology theories. I'll
focus on the uncolored case and I'll sketch proof of invariance.

17.00
 Melissa Zhang* 
lecture 3: A perspective on annular Khovanov homology
lecture notes
video
A link \(L\) living in a thickened annulus \((\mathbb{R}^2 \smallsetminus \{0\})\times[0,1]\) is called an annular link. The ambient space equips the bigraded Khovanov chain complex of \(L\) with an additional annular (filtration) grading, and the associated graded complex computes the annular Khovanov homology, AKh(\(L\)). Understanding annular knots and links is important in many different contexts in lowdimensional topology; this lecture series will survey some existing and potential relationships between AKh and contact topology, knot concordance, representation theory, and more.
Some familiarity with Khovanov homology at the level of Dror BarNatan's introductory paper on Khovanov homology is recommended. Fun computational exercises will be provided.

Thursday 
10.30
 Andrew Lobb\(^\dagger\) 
lecture 4: Spectral Sequences and Khovanov homology
lecture notes
video
We see a bit of the OzsváthSzabó spectral sequence, the KronheimerMrowka spectral sequence, and we discuss two filtrations on a homology of strongly invertible knots.

11.30
 Q&A session on zoom

13.30
 Paul Wedrich 
lecture 3: Invariants of 4manifolds from KhovanovRozansky link homology
video
Lecture 3 will be about 'Categorified Kauffman trick and its applications; 4manifold skein modules (status quo)'.
For lecture notes, please contact Paul directly via email.

14.30
 Q&A session discord/exercise session

15.45
 LouisHadrien Robert 
lecture 4: gl(N) link homology via foams
lecture notes (all in one)
video
I'll give an overview of some other link homology theories
called symmetric link homology. They use the same foams evaluation
technique but in an annular setting.

17.00
 Melissa Zhang* 
lecture 4: A perspective on annular Khovanov homology
lecture notes
video
A link \(L\) living in a thickened annulus \((\mathbb{R}^2 \smallsetminus \{0\})\times[0,1]\) is called an annular link. The ambient space equips the bigraded Khovanov chain complex of \(L\) with an additional annular (filtration) grading, and the associated graded complex computes the annular Khovanov homology, AKh(\(L\)). Understanding annular knots and links is important in many different contexts in lowdimensional topology; this lecture series will survey some existing and potential relationships between AKh and contact topology, knot concordance, representation theory, and more.
Some familiarity with Khovanov homology at the level of Dror BarNatan's introductory paper on Khovanov homology is recommended. Fun computational exercises will be provided.

Friday 
13.30
 Paul Wedrich 
lecture 4: Invariants of 4manifolds from KhovanovRozansky link homology
video
Lecture 4 is entitled 'Properties and computations of 4manifold skein modules'.
For lecture notes, please contact Paul directly via email.

14.30
 Q&A session discord/exercise session

15.30
 Jacob Rasmussen* 
Between Floer and Khovanov
slides
video
At first sight, the definitions of Heegaard Floer homology and Khovanov homology seem quite
different, but there are many surprising analogies between them. The strategy of finding and
exploiting these similarities has been around for almost 20 years now, but remains relevant. I’ll
describe some past successes of this method together with some prospects for future research.

Saturday 
10.30
 Marco Marengon* 
A generalization of Rasmussen’s invariant, with applications to surfaces in
some fourmanifolds
slides
video
We extend the definition of KhovanovLee homology to links in connected sums of \(S^1\times S^2\), and construct a Rasmussentype invariant for nullhomologous links in these manifolds. For certain links in \(S^1\times S^2,\) we compute the invariant by reinterpreting it in terms of Hochschild homology. As applications, we prove inequalities relating the Rasmussentype invariant to the genus of surfaces with boundary in the following fourmanifolds: \(B^2\times S^2\), \(S^1\times B^3\), \(\mathbb{C}P^2\), and various connected sums and boundary sums of these. We deduce that Rasmussen's invariant also gives genus bounds for surfaces inside homotopy fourballs obtained from \(B^4\) by a certain operation called Gluck twists. Therefore, Rasmussen’s invariant cannot be used to prove that such homotopy fourballs are nonstandard.

11.50
 Cristina Anghel* 
Coloured Jones and Alexander polynomials unified through Lagrangian intersections in configuration spaces
slides
video
The theory of quantum invariants started with the Jones polynomial and continued with the ReshetikhinTuraev algebraic construction of link invariants.
In this context, the quantum group \(U_q (sl(2))\) leads to the sequence of coloured Jones
polynomials, which contains the original Jones polynomial.
Dually, the quantum group at roots of unity gives the sequence of coloured Alexander polynomials.
We construct a unified topological model for these two sequences of quantum invariants. More specifically, we define certain homology classes given by Lagrangian submanifolds in configuration spaces.
Then, we prove that the \(N\)th coloured Jones and \(N\)th coloured Alexander invariants come as different specialisations of a state
sum (defined over 3 variables) of Lagrangian intersections in configuration spaces.
As a particular case, we see both Jones and Alexander polynomials from the same
intersection pairing in a configuration space.

14.00
 Artem Kotelskiy* 
Khovanov homology via Floer theory of the 4punctured sphere
slides
video
Consider a Conway twosphere \(S\) intersecting a knot \(K\) in 4 points, and thus decomposing the knot into two 4ended tangles, \(T\) and \(T'\). We will first interpret Khovanov homology \(\mathrm{Kh}(K)\) as Lagrangian Floer homology of a pair of specifically constructed immersed curves \(\mathrm{Kh}(T)\) and \(\mathrm{BN}(T')\) on the dividing 4punctured sphere \(S\). Next, motivated by tanglereplacement questions in knot theory, we will describe a recently obtained structural result concerning the curve invariant \(\mathrm{Kh}(T)\), which severely restricts the types of curves that may appear as tangle invariants. The proof relies on the matrix factorization framework of KhovanovRozansky, as well as the homological mirror symmetry statement for the 3punctured sphere. This is joint work with Liam Watson and Claudius Zibrowius.

15.20
 Liam Watson* 
Heegaard Floer homology and separating tori
slides
video
Towards placing some of the material from Artem Kotelskiy’s talk in context, I will discuss some older joint work with Jonathan Hanselman and Jake Rasmussen. This will centre on the following result: A closed orientable threemanifold containing a separating torus has (the hat version of it's) Heegaard Floer homology of dimension at least 5. The talk aims to give and overview of the proof and discuss consequences, and perhaps even tie in with Jake Rasmussen’s talk, which opened the conference.

16.10
 Akram Alishahi* 
Braid invariant related to knot Floer homology and Khovanov homology
video
Knot Floer homology and Khovanov homology are homological knot invariants that are defined using very different methods — the former is a Lagrangian Floer homology, while the latter has roots in representation theory. Despite these differences, the two theories contain a great deal of the same information and were conjectured by Rasmussen to be related by a spectral sequence. This conjecture was recently proved by Dowlin, however, his proof is not computationally effective. In this talk we will sketch a local framework for proving this conjecture. To do that, we will describe an algebraic/combinatorial glueable braid invariant which using a specific closing up operation results in a knot invariant related by a spectral sequence to Khovanov homology. Moreover, it is chain homotopic to Ozsvath–Szabo's braid invariants which using their closing up operation recovers knot Floer homology. If time permits we will compare the two closing up operations. This is joint work with Nathan Dowlin.

Sunday 
10.30
 Krzysztof Putyra* 
Towards a spectral sequence from HOMFLYPT to HeegaardFloer knot homology
pdf notes
interactive notes
video
The beauty of the HOMFLYPT polynomial is that it generalizes all \(\mathrm{sl}(N)\) link
polynomials as well as the AlexanderConway polynomial. In the categorified
setting the analogous relation has been found by Rasmussen in the form of a spectral
sequence from the categorified HOMFLYPT to \(\mathrm{sl}(N)\) link homology for all \(N > 0\).
However, a similar relation to the categorified AlexanderConway polynomial,
the HeegaardFloer knot homology, is currently unknown, although the results
of Manolescu and Dowlin suggests that such a spectral sequence should exist.
In my talk I will show how to construct a spectral sequence (over a field of
characteristic other than 2) from the reduced HOMFLYPT homology to a certain
homology of a knot diagram that coincides with HFK over \(\mathbb{Z}/2\).
This is joint work with Anna Beliakova, LouisHadrien Robert and Emmanuel Wagner.

11.50
 Hoel Queffelec* 
Surface skein algebras, categorification and positivity
notes
video
Skein algebra for surfaces are natural generalizations of the Jones polynomial to thickened surfaces. Khovanov homology can be extended beyond the 3sphere following a similar process, but the algebra structure is trickier to understand at the categorical level, partly because of the lack of functoriality of Khovanov's original construction. I'll review ways to understand the skein category of a surface, and explain how we're trying to use these tools to prove a conjecture by FockGoncharovThurston claiming that the skein algebras have positive structure constants.
This is joint work with Kevin Walker and Paul Wedrich.

* speaker will join virtually
\(^\dagger\) streaming of prerecorded video
programme/schedule as pdf
Due to the COVID19 pandemic, we have decided to carry out the workshop as a hybrid event, partially online and partially in person. Our intention is to host some talks virtually and others physically in Regensburg. All talks will be streamed online.
Before finalizing your travel plans, we would like to ask you to wait until we confirm that you can indeed participate in person. Moreover, it is your own responsibility to check which travel restrictions apply to you. As far as we understand, the rules as of 28 June 2021 can be summarized as follows: (No guarantees. Please check for yourself!)
Generally speaking, entry to Germany is only permitted if you are

fully vaccinated or

come from the European Union, the Schengen Area, or a country on a safe list; this list currently includes Australia, Japan, and the United States (among others).
Moreover, you cannot enter Germany if you come from an area of virus variants of concern; these areas currently include Brazil, India, Portugal, Russia, and the United Kingdom.
You only need to quarantine if you are not fully vaccinated and come from a risk area; these areas currently include the Netherlands, Spain, Turkey, and some parts of Ireland and Sweden. A complete list can be found here.
For full details, see this link.
examples: (Again, no guarantees. Please check for yourself!)
If you travel from the US, you can travel to Germany without quarantining.
The same applies if you travel from Canada and are fully vaccinated.
If you are currently in the United Kingdom, you can only participate online.
If you arrive from China, you are currently not allowed to enter Germany, but this might change in the foreseeable future.
We advise that you do not make any bookings before we have confirmed that you can indeed participate.
Directions for travel to the University of Regensburg can be found here.
Local Info Handout
Participants will be responsible for arranging their own accommodation. If you are interested in sharing accommodation and/or coordinating your travel plans with other participants, please allow us to share your contact details by ticking the appropriate box during your registration.
budget options for accommodation
hotels
Here is a list of participants. (S) after the name indicates that that person is a workshop lecturer or a conference speaker; (C) means that the person only registered for the conference.
 Leonard Okyere Afeke, University of Toronto
 Akram Alishahi (S), University of Georgia, Athens
 Cristina Anghel (S), University of Oxford
 Jai Aslam, North Carolina State University
 Rhea Palak Bakshi, The George Washington University
 Wang Bangxin, University of Zurich
 Anna Beliakova, University of Zurich
 Fraser Binns, Boston College
 Holt Bodish, University of Oregon
 Jennifer Brown, UC Davis
 Federico Cantero Morán (C), Universidad Autónoma de Madrid
 Jacob Caudell, Boston College
 Nafaa Chbili (C), United Arab Emirates University
 Carlo Collari, NYUAD
 Sjoerd de Vries, University of Bonn
 Jesse Frohlich (C), University of Toronto
 D. Zack Garza, University of Georgia
 Paul Großkopf, Université libre de Bruxelles
 Onkar Gujral, MIT
 Quoc Ho, IST Austria
 Tom Hockenhull, MPIM Bonn
 Marius Huber, Boston College
 Dionne Ibarra, The George Washington University
 Damian Iltgen, University of Regensburg
 Dorota Jankowska, University of Warsaw
 Homayun Karimi (C), McMaster University
 Marc Kegel (C), Humboldt Universität Berlin
 Nadezhda Khoroshavkina, HSE University
 Nitu Kitchloo, Johns Hopkins University
 Artem Kotelskiy (S), University of Indiana, Bloomington
 Pravin Kumar V, IISER Mohali, India
 Deniz Kutluay (C), Indiana University
 Xiaobin Li, Southwest Jiaotong University
 Wenbo Liao, Southern University of Science and Technology, China
 Andrew Lobb (S), Durham University
 Georgy Luke, IISER Tirupati
 Marco Marengon (S), MPIM Bonn
 Clément Maria (C), INRIA
 Laura Marino, University of Regensburg
 Aaron MazelGee, Caltech
 Ian Montague, Brandeis University
 Allison Moore (C), Virginia Commonwealth University
 Lars Munser, University of Regensburg
 Gregoire Naisse, MPIM Bonn
 Neha Nanda, Indian Institute of Science Education and Research Mohali
 Sergey Nersisyan, Princeton University
 Kie Seng Nge (C), Australian National University
 Jakub Paliga, University of Warsaw
 Martin Palmer, Mathematical Institute of the Romanian Academy, Bucharest
 Krzysztof Putyra (S), University of Zurich
 Hoel Queffelec (S), Institut Montpelliérain Alexander Grothendieck
 José Pedro Quintanilha, University of Regensburg
 Jake Rasmussen (S), University of Cambridge
 Isaac Ren (C), Inria Sophia Antipolis
 LouisHadrien Robert (S), Université du Luxembourg
 Christopher Roque (C), Centro de Ciencias Matemáticas UNAM
 Benjamin Matthias Ruppik, MPIM Bonn
 William Rushworth (C), McMaster University
 Pablo Sanchez Ocal, Texas A and M University
 Oguz Savk, Bogazici University
 Radmila Sazdanovic (C), NC State University
 Léo Schelstraete, UCLouvain
 Dirk Schuetz (C), Durham University
 Manpreet Singh, Indian Institute of Science Education and Research Mohali
 Kai Smith, Indiana University
 Devaux Steven, Université de Montpellier
 Charles Stine, Brandeis University
 Haoyu Sun (C), UT Austin
 Pedro Tamaroff, Trinity College Dublin
 Paula Truöl, ETH Zurich
 Pedro Vaz (C), Universite catholique de Louvain
 Vogelmann Vivien, University of Freiburg
 Mingjie Wang (C), Southern University of Science and Technology
 Liam Watson (S), University of British Columbia
 Ben Webster (C), University of Waterloo and Perimeter Institute
 Paul Wedrich (S), Max Planck Institute for Mathematics, Bonn
 Fan Ye, University of Cambridge
 Melissa Zhang (S), University of Georgia, Athens
 Xuan Zhao (C), Beijing Normal University
Technical advice for hybrid conferences
We used the following platforms:

Zoom for live talks

Discord for chatting

Mediathek, a website of University of Regensburg, to share videos

Grips, the moodle elearning system run by the University of Regensburg, to share all other material
To get an impression, check out our videos and an example video of a blackboard talk
Microphones
We had a Lavalier microphone (to clip on the shirt) for the local speaker giving a blackboard talk, plus a handheld microphone for the chair, and to pass around the audience for questions. Both of those microphones were wireless. To be able to connect two microphones at once to one laptop, we used a USB audio interface with two inputs.
The microphones we used needed to be recharged after 2–3 hours of use (they would reliably last for one talk, but not for two). So we used two sets of Lavalier microphones, and charged one while using the other.
The microphones each have a sender and a receiver, which look very similar, but are not interchangeable. Look at the small icon on the back to tell which is which.
The handheld microphone should be held close to the mouth for good quality.
Loudspeakers
For the audio output, we used the audio system (loudspeakers) of the lecture hall, connected to the laptop via HDMI. During blackboard talks, the audio output was for questions coming from the zoom audience. The speaker, the chair, and questions from the physical room were not going through the loudspeakers.
Cameras
We used two cameras: one directed at the speaker and the blackboard, the other directed at the audience.
Regarding the first camera, the resolution of the standard zoom video stream is often too poor for blackboard talks. But there is a fix! Simply use the option share second camera in the extended menu for screen sharing; this results in a much better resolution (for the price of a reduced frame rate). The blackboard camera was set up such that two whole blackboards were visible when stacked one above the other, such that we did not have to move it during the talks.
To avoid trapezoid distortion, we made sure that the plane of the camera lens is parallel to the plane of the blackboard (in particular, if the camera is too low, instead of pointing the camera upwards, we rather positioned the whole camera higher up; overhead projectors make very good camera stands). Also, we set the focus at the beginning of the conference (the camera has a button for this), so that writing on the blackboard would be in focus, and disabled the camera's continuous autofocus (the camera has a slider for this).
The second camera was plugged in a tablet or laptop on the speaker's desk. The camera allows the online participants to see the onsite participants. The table/laptop allows the speaker to see their own video.
Projectors
We used one projector in the lecture hall to present the slides of the speaker, for slide talks by onsite speakers or speakers joining via zoom.
The second projector in the room showed the Zoom page of the meeting with the online participants. This allows onsite participants to see online participants; combined with the camera directed at the audience, this means that all participants can see each other.
Laptop
If you follow our setup, you will have one laptop with lots of devices attached. It's easiest if you operate that laptop from the lecture hall's front or second row, and not from the table in front of the blackboards. For that reason you might need various extensions cords.
Recording
For higher flexibility, it is recommendable to record the zoom meeting to the Cloud rather than on this Computer. Try to avoid having to edit the video if possible, because that may be quite time consuming. So, make sure that the recording is started and stopped at the correct moment (in particular if the chair is not the person operating the zoom laptop).
Check in advance whether the website to which you are going to upload the videos has a maximal resolution (e.g. in case of the mediathek of the University of Regensburg, this is 1920 x 1080). If a zoom speaker is sharing their screen with a higher resolution, one can ask them to lower their screen's resolution; otherwise, one needs to change the resolution of the recording afterwards, which takes quite a lot of computing time.
Zoom
If you arrange the Zoom meeting for your conference, then do not choose the option Only authenticated users can join meetings / Nur für authentifizierte Benutzer zulassen. This option will only allow participants which have a valid Zoom license and you might have participants which cannot access the meeting because of this.
Moodle (called grips in Regensburg)
One may open a moodle course to passwordprotected guest access for participants without UR accounts. For this, in the grips course, go to Actions Menu / Users / Enrolment Methods / Guest access. You can share the link to the grips course with the participants, and they can access it by clicking Log in as a guest / Confirm Site policy agreement / Enter password.
Discord
We set up a discord server for the workshop with one channel for each lecture course (plus a general one for announcements, introductions, etc.). These were used not only by the online participants, but also by some local people.
Technical support
A student from the IT support helped us with the technical setup and was in charge of the host laptop during the zoom talks. This allowed us to focus more on the content of the lectures and on managing questions and comments from the audience.
Some things that did not work for us

It is tempting to try to connect several laptops in the lecture hall to zoom, in order to use the microphones of those additional laptops. However, if you are using the loudspeakers of the lecture for output, the additional laptops will pick up that output, and there will be feedback (resulting in a screeching noise). The only way to avoid this seems to be to have all audio input going to one single laptop (which is how we set it up).

We considered replacing zoom by other programs, but found it to be the best option in the end. Jitsi and discord seemed less reliable (note that we still used discord, but only for chatting, not for the live talks); the streaming on twitch is in high quality, but twitch streams are always public, and viewers can only interact via chat (not video of their own). We did not test BigBlueButton.

Using one microphone for the whole room would be much easier, but did not result in acceptable audio quality.
What could be improved

Having only one handheld microphone to pass around the audience for questions can be cumbersome (and also problematic in view of the pandemic). However, having more microphones would make the setup more expensive and more complex (e.g. it would require a USB audio interface with more than two inputs).
General advice

Test your technical setup some days in advance.

For speakers joining via zoom, make short technical tests to make sure their setup works.

During the event, plan enough time (at least 30min) to set everything up in the lecture hall.
List of material

A laptop for hosting the zoom meeting, a second laptop or tablet for the speaker and the second camera

2 x Sennheiser XSWD Portable Lavalier Set

Sennheiser XSWD Vocal Set (the handheld microphone)

USBC chargers for the microphones (each microphone has one, but consider bringing more, because each microphone needs two (sender and receiver))

2 x IPEVO V4 K Ultra High Definition USB Document Camera

Focusrite Scarlett Solo (USB soundcard to plug in two microphones at once)

Various 3 or 5 meter extension cords (for electricity, USB, HDMI, audio jack)

USB multi plug
