This is an overview of themes for the Learning Sessions (31 July - 4 August 2017) that will be part of the program Genealogies of Interacting Particle Systems at the Institute for Mathematical Sciences of the National University of Singapore. Based on the preferences of participants, we have chosen nine learning sessions that will be organized. The intended format of the Learning Sessions is briefly explained on the webpages of the program. Two people (moderators) together prepare an introduction to the topic in the form of an introductory lecture of (roughly) 90 minutes and formulate questions and problems to be discussed in the session. Moderators should have a genuine interest in learning the topic but not be authors of the papers to be studied.

**Genealogies of particles on dynamic random networks**Moderators:*Anton Klimovsky*and*Jiří Černý*. Motivated, e.g., by complex network modelling and statistical issues like inference of network model parameters. One could try to learn more about graph limits, sparse graphs vs. exchangeability, dynamic random network models (graph-valued Markov processes), and explore e.g., open questions on particle systems in the spirit of Aldous' "Interacting particle systems as stochastic social dynamics" in the context of time-varying underlying network models. Based on, e.g.,- Aldous, David. "Interacting particle systems as stochastic social dynamics." Bernoulli 19.4 (2013): 1122-1149.
- Crane, Harry. "Time-varying network models." Bernoulli 21.3 (2015): 1670-1696.
- Crane, Harry. "Dynamic random networks and their graph limits." The Annals of Applied Probability 26.2 (2016): 691-721.
- Borgs, Christian, et al. "Sparse exchangeable graphs and their limits via graphon processes." arXiv preprint arXiv:1601.07134 (2016).
- Avena, Luca, et al. "Mixing times of random walks on dynamic configuration models." arXiv preprint arXiv:1606.07639 (2016).

**The Brownian web and net**Moderators:*Vlada Limic*and*Nic Freeman*. Based, e.g., on:- E. Schertzer, R. Sun and J.M. Swart. The Brownian web, the Brownian net, and their universality. (arXiv:1506.00724) Advances in Disordered Systems, Random Processes and Some Applications, 270--368, Cambridge University Press, 2017.
- L.R.G. Fontes, M. Isopi, C.M. Newman, K. Ravishankar. The Brownian web: characterization and convergence. Ann. Probab. 32(4), 2857{2883, 2004.
- R. Sun and J.M. Swart. The Brownian net. Ann. Probab. 36, 1153-1208, 2008.
- C.M. Newman, K. Ravishankar, and E. Schertzer. Marking (1,2) points of the Brownian web and applications. Ann. Inst. Henri Poincaré Probab. Statist. 46, 537-574, 2010.
- E. Schertzer, R. Sun and J.M. Swart (2010): Stochastic flows in the Brownian web and net. (Mem. Am. Math. Soc. Vol. 227 (2013), Nr. 1065)

**Extremal particles in Branching Brownian Motion**Moderators:*Sandra Kliem*and*Kumarjit Saha*. This could be based on recent work of the Berestycki brothers and Schweinsberg, as well as Maillard, on Branching Brownian motion with a moving boundary:- J. Berestycki, N. Berestycki, and J. Schweinsberg. The genealogy of branching Brownian motion with absorption. Ann. Probab. 41(2) (2013), 527–618.
- P. Maillard. Speed and fluctuations of N-particle branching Brownian motion with spatial selection. Preprint (2013), 74 pages, ArXiv:1304.0562v2
- Arguin, Bovier & Kistler, The genealogy of extremal particles of Branching Brownian Motion. CPAM, 64, (2011)

- A. Bovier. From spin glasses to branching Brownian motion--and back? (Lecture notes for a course given at the 7th Prague Summer School on Mathematical Statistical Mechanics, August 19--30, 2013).

**Competing species models**Moderators:*Matthias Hammer*and*Yu-Ting Chen*. Based, e.g., on:- C. Neuhauser and S.W. Pacala. An explicitly spatial version of the Lotka–Volterra model with interspecific competition. Ann. Appl. Probab. 9, (1999), 1226–1259.
- A. Sturm and J.M. Swart (2007): Voter models with heterozygosity selection. (Ann. Appl. Probab. 18 No. 1 (2008), 59-99)
- J. Blath, A.M. Etheridge and M.E. Meredith. Coexistence in locally regulated competing populations and survival of BARW. Ann. Appl. Probab. 17, (2007), 1474–1507.

**Dualities in population models**Moderators:*Daniel Valesin*,*Fernando Cordero*, and*Stein Andreas Bethuelsen*. Possible suggested references (*non binding*):- D.A. Dawson and A. Greven. Spatial Fleming-Viot models with selection and mutation. Lecture Notes in Mathematics 2092. Springer (2014) 856 pages.
- A. Sturm and J.M. Swart. Pathwise duals of monotone and additive Markov processes. J. Theor. Probab. (2016). doi:10.1007/s10959-016-0721-5. 52 pages.
- M. Hutzenthaler and R. Alkemper. Graphical representation of some duality relations in stochastic population models. Electron. Commun. Probab. 12 (2007), 206–220.
- J.M. Swart (2006): Duals and thinnings of some relatives of the contact process. (18 pages) arXiv:math.PR/0604335.

**The algebraic approach to duality**Moderators:*Anja Sturm*and*Florian Völlering*. Based, e.g., on:- C. Giardinà, J. Kurchan, F. Redig, K. Vafayi. Duality and hidden symmetries in interacting particle systems. Journal of Statistical Physics 135(1), (2009), 25–55.
- G. Carinci, C. Giardinà, C. Giberti, F. Redig. Dualities in population genetics: a fresh look with new dualities. ArXiv:1302.3206 (2013). appeared SPA.
- A. Sudbury. Dual families of interacting particle systems on graphs. J. Theor. Probab. 13(3), (2000), 695-716.

**Look down constructions**Moderators:*Amandine Véber*and*Anton Wakolbinger*. Based, e.g., on:- P. Donnelly and T. Kurtz (1999), Particle representations for measure-valued population models, Ann. Probab. 27 , no. 1, 166–205.
- T. Kurtz and E. Rodrigues (2011),, Poisson representations of branching Markov and measure-valued branching processes, Ann. Probab. 39 939-984.
- A. Etheridge and T. Kurtz (2016), Genealogical constructions of population models

**Tree-valued Markov processes**Moderators:*Andrej Depperschmidt*and*Andreas Greven*. The following suggestion was made for the theme "Look-down constructions" but perhaps fits better here?- The approach of Le Gall and Bertoin (flows of bridges). Indeed, the latter approach provides an alternative way of (1) coupling Fleming-Viot dynamics with their underlying genealogies, (2) constructing tree-values processes. There is also a nice article by Cyril Labbe connecting Look-down constructions with flows of bridges (``From flows of ΛΛ-Fleming-Viot processes to lookdown processes via flows of partitions'').

**The Continuum Random Tree**Moderators:*Anita Winter*and*Emmanuel Schertzer*. Based on, e.g.,- Pitman, Enumerations of trees and forests related to branching processes and random walks, Microsurveys in discrete probability (1997) (for a proof that particular GW-trees conditioned on number of vertices are uniform ordered/binary/unordered, labelled trees = OtterDwass-Formel)
- Aldous, Continuum random tree III, AoP 1993, (for the definition and a proof of convergence of suitably rescaled GW trees conditioned on the number of vertices towards the CRT)
- Marckert & Mokkadem, The depth first process of Galton-Watson trees converge to the same Brownian excursion, AoP, 2003 (for another proof which uses Contour functions, Height function and the Lukaciewiec walk)
- Bennies & Kersting, A random walk approach to Galton-Watson trees, Journal of theoretical probability, 2000 (alternative to the previous paper, but slightly weaker)
- Bertoin & Miermont, The cut-tree of large Galton-Watson trees and the Brownian CRT, AoP 2013 (traces back the genealogy of parition elements of the CRT obtained by letting rain down cut points/mutations on the CRT; proof makes use of the additive coalescent) and shows that the cut tree is again a CRT)
- Possibly also include splitting trees - see ``The contour of splitting trees is a Lévy process'' of Lambert - and their connections to the coalescent point processes of Popovic and Aldous.