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 two-day research conference.

poster       health and safety measures

• venue Faculty of Mathematics, University of Regensburg/online
• workshop lecturers
  • Andrew Lobb, Durham University
  • Louis-Hadrien Robert, Université du Luxembourg
  • Paul Wedrich, Max Planck Institute for Mathematics, Bonn
  • Melissa Zhang, University of Georgia, Athens
• special lecturer
  • Jacob Rasmussen, University of Cambridge
• 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
  • Lukas Lewark, University of Regensburg
  • Claudius Zibrowius, University of Regensburg

If you have any questions or concerns about the event, please contact the organizers at perspectives2021\(@\)posteo.net.

This event is funded by the SFB 1085 Higher Invariants.

The svg-icons 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
14.30	coffee & tea & registration
15.30	Louis-Hadrien 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.
16.30	break
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 low-dimensional 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 Bar-Natan's introductory paper on Khovanov homology is recommended. Fun computational exercises will be provided.
Tuesday
10.00	coffee & tea
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
12.00	lunch
13.30	Paul Wedrich | lecture 1: Invariants of 4-manifolds from Khovanov-Rozansky link homology video Ribbon categories are 3-dimensional algebraic structures that control quantum link polynomials and that give rise to 3-manifold invariants known as skein modules. I will describe how to use Khovanov-Rozansky link homology, a categorification of the gl(N) quantum link polynomial, to obtain a 4-dimensional algebraic structure that gives rise to vector space-valued invariants of smooth 4-manifolds, following this paper with Scott Morrison and Kevin Walker. Lecture 1 will be on 'Khovanov-Rozansky gl(N) link homology: introduction, functoriality'. For lecture notes, please contact Paul directly via email.
14.30	Q&A session discord/exercise session
15.30	break
15.45	Louis-Hadrien 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.
16.45	break
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 low-dimensional 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 Bar-Natan's introductory paper on Khovanov homology is recommended. Fun computational exercises will be provided.
Wednesday
10.00	coffee & tea
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
12.00	lunch
13.30	Paul Wedrich | lecture 2: Invariants of 4-manifolds from Khovanov-Rozansky link homology video Lecture 2 will be about 'Khovanov-Rozansky gl(N) link homology: properties, diagram independence'. For lecture notes, please contact Paul directly via email.
14.30	Q&A session discord/exercise session
15.30	break
15.45	Louis-Hadrien 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.
16.45	break
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 low-dimensional 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 Bar-Natan's introductory paper on Khovanov homology is recommended. Fun computational exercises will be provided.
Thursday
10.00	coffee & tea
10.30	Andrew Lobb\(^\dagger\) | lecture 4: Spectral Sequences and Khovanov homology lecture notes       video We see a bit of the Ozsváth-Szabó spectral sequence, the Kronheimer-Mrowka spectral sequence, and we discuss two filtrations on a homology of strongly invertible knots.
11.30	Q&A session on zoom
12.00	lunch
13.30	Paul Wedrich | lecture 3: Invariants of 4-manifolds from Khovanov-Rozansky link homology video Lecture 3 will be about 'Categorified Kauffman trick and its applications; 4-manifold skein modules (status quo)'. For lecture notes, please contact Paul directly via email.
14.30	Q&A session discord/exercise session
15.30	break
15.45	Louis-Hadrien 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.
16.45	break
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 low-dimensional 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 Bar-Natan's introductory paper on Khovanov homology is recommended. Fun computational exercises will be provided.
Friday
13.30	Paul Wedrich | lecture 4: Invariants of 4-manifolds from Khovanov-Rozansky link homology video Lecture 4 is entitled 'Properties and computations of 4-manifold skein modules'. For lecture notes, please contact Paul directly via email.
14.30	Q&A session discord/exercise session
15.15	break
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.
16.30	reception
Saturday
10.00	coffee & tea
10.30	Marco Marengon* | A generalization of Rasmussen’s invariant, with applications to surfaces in some four-manifolds slides       video We extend the definition of Khovanov-Lee homology to links in connected sums of \(S^1\times S^2\), and construct a Rasmussen-type invariant for null-homologous 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 Rasmussen-type invariant to the genus of surfaces with boundary in the following four-manifolds: \(B^2\times S^2\), \(S^1\times B^3\), \(\mathbb{C}P^2\), and various connected sums and boundary sums of these. We deduce that Rasmussen's invariant also gives genus bounds for surfaces inside homotopy four-balls obtained from \(B^4\) by a certain operation called Gluck twists. Therefore, Rasmussen’s invariant cannot be used to prove that such homotopy four-balls are non-standard.
11.20	break
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 Reshetikhin-Turaev 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.
12.40	lunch
14.00	Artem Kotelskiy* | Khovanov homology via Floer theory of the 4-punctured sphere slides       video Consider a Conway two-sphere \(S\) intersecting a knot \(K\) in 4 points, and thus decomposing the knot into two 4-ended 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 4-punctured sphere \(S\). Next, motivated by tangle-replacement 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 Khovanov-Rozansky, as well as the homological mirror symmetry statement for the 3-punctured sphere. This is joint work with Liam Watson and Claudius Zibrowius.
14.50	break
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 three-manifold 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
10.00	coffee & tea
10.30	Krzysztof Putyra* | Towards a spectral sequence from HOMFLYPT to Heegaard-Floer 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 Alexander-Conway 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 Alexander-Conway polynomial, the Heegaard-Floer 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, Louis-Hadrien Robert and Emmanuel Wagner.
11.20	break
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 3-sphere 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 Fock-Goncharov-Thurston 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 COVID-19 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

• B&B Regensburg
• Youth Hostel
• City Hostel
• bedandbreakfast.eu
• Airbnb

hotels

• Hotel Ibis Regensburg City
• Münchener Hof
• Kaiserhof am Dom

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 Mazel-Gee, 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
• Louis-Hadrien 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
• Xu-an 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 e-learning 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 password-protected 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 XSW-D Portable Lavalier Set
• Sennheiser XSW-D Vocal Set (the handheld microphone)
• USB-C 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