The Simons Observatory (SO) is a ground-based cosmic microwave background (CMB) experiment sited on Cerro Toco in the Atacama Desert in Chile that promises to provide breakthrough discoveries in fundamental physics, cosmology, and astrophysics. Supported by the Simons Foundation, the Heising-Simons Foundation, and with contributions from collaborating institutions, SO will see first light in 2021 and start a five year survey in 2022. SO has 287 collaborators from 12 countries and 53 institutions, including 85 students and 90 postdocs. The SO experiment in its currently funded form ('SO-Nominal') consists of three 0.4 m Small Aperture Telescopes (SATs) and one 6 m Large Aperture Telescope (LAT). Optimized for minimizing systematic errors in polarization measurements at large angular scales, the SATs will perform a deep, degree-scale survey of 10% of the sky to search for the signature of primordial gravitational waves. The LAT will survey 40% of the sky with arc-minute resolution. These observations will measure (or limit) the sum of neutrino masses, search for light relics, measure the early behavior of Dark Energy, and refine our understanding of the intergalactic medium, clusters and the role of feedback in galaxy formation. With up to ten times the sensitivity and five times the angular resolution of the Planck satellite, and roughly an order of magnitude increase in mapping speed over currently operating ("Stage 3") experiments, SO will measure the CMB temperature and polarization fluctuations to exquisite precision in six frequency bands from 27 to 280 GHz. SO will rapidly advance CMB science while informing the design of future observatories such as CMB-S4.

The Simons Observatory Collaboration Maximilian H. Abitbol Shunsuke Adachi Peter Ade James Aguirre Zeeshan Ahmed Simone Aiola Aamir Ali David Alonso Marcelo A. Alvarez Kam Arnold Peter Ashton Zachary Atkins Jason Austermann Humna Awan Carlo Baccigalupi Taylor Baildon Anton Baleato Lizancos Darcy Barron Nick Battaglia Richard Battye Eric Baxter Andrew Bazarko James A. Beall Rachel Bean Dominic Beck Shawn Beckman Benjamin Beringue Tanay Bhandarkar Sanah Bhimani Federico Bianchini Steven Boada David Boettger Boris Bolliet J. Richard Bond Julian Borrill Michael L. Brown Sarah Marie Bruno Sean Bryan Erminia Calabrese Victoria Calafut Paolo Calisse Julien Carron Fred. M Carl Juan Cayuso Anthony Challinor Grace Chesmore Yuji Chinone Jens Chluba Hsiao-Mei Sherry Cho Steve Choi Susan Clark Philip Clarke Carlo Contaldi Gabriele Coppi Nicholas F. Cothard Kevin Coughlin Will Coulton Devin Crichton Kevin D. Crowley Kevin T. Crowley Ari Cukierman John M. D'Ewart Rolando Dünner Tijmen de Haan Mark Devlin Simon Dicker Bradley Dober Cody J. Duell Shannon Duff Adri Duivenvoorden Jo Dunkley Hamza El Bouhargani Josquin Errard Giulio Fabbian Stephen Feeney James Fergusson Simone Ferraro Pedro Fluxà Katherine Freese Josef C. Frisch Andrei Frolov George Fuller Nicholas Galitzki Patricio A. Gallardo Jose Tomas Galvez Ghersi Jiansong Gao Eric Gawiser Martina Gerbino Vera Gluscevic Neil Goeckner-Wald Joseph Golec Sam Gordon Megan Gralla Daniel Green Arpi Grigorian John Groh Chris Groppi Yilun Guan Jon E. Gudmundsson Mark Halpern Dongwon Han Peter Hargrave Kathleen Harrington Masaya Hasegawa Matthew Hasselfield Makoto Hattori Victor Haynes Masashi Hazumi Erin Healy Shawn W. Henderson Brandon Hensley Carlos Hervias-Caimapo Charles A. Hill J. Colin Hill Gene Hilton Matt Hilton Adam D. Hincks Gary Hinshaw Renée Hložek Shirley Ho Shuay-Pwu Patty Ho Thuong D. Hoang Jonathan Hoh Selim C. Hotinli Zhiqi Huang Johannes Hubmayr Kevin Huffenberger John P. Hughes Anna Ijjas Margaret Ikape Kent Irwin Andrew H. Jaffe Bhuvnesh Jain Oliver Jeong Matthew Johnson Daisuke Kaneko Ethan D. Karpel Nobuhiko Katayama Brian Keating Reijo Keskitalo Theodore Kisner Kenji Kiuchi Jeff Klein Kenda Knowles Anna Kofman Brian Koopman Arthur Kosowsky Nicoletta Krachmalnicoff Akito Kusaka Phil LaPlante Jacob Lashner Adrian Lee Eunseong Lee Antony Lewis Yaqiong Li Zack Li Michele Limon Eric Linder Jia Liu Carlos Lopez-Caraballo Thibaut Louis Marius Lungu Mathew Madhavacheril Daisy Mak Felipe Maldonado Hamdi Mani Ben Mates Frederick Matsuda Loïc Maurin Phil Mauskopf Andrew May Nialh McCallum Heather McCarrick Chris McKenney Jeff McMahon P. Daniel Meerburg James Mertens Joel Meyers Amber Miller Mark Mirmelstein Kavilan Moodley Jenna Moore Moritz Munchmeyer Charles Munson Masaaki Murata Sigurd Naess Toshiya Namikawa Federico Nati Martin Navaroli Laura Newburgh Ho Nam Nguyen Andrina Nicola Mike Niemack Haruki Nishino Yume Nishinomiya John Orlowski-Scherer Luca Pagano Bruce Partridge Francesca Perrotta Phumlani Phakathi Lucio Piccirillo Elena Pierpaoli Giampaolo Pisano Davide Poletti Roberto Puddu Giuseppe Puglisi Chris Raum Christian L. Reichardt Mathieu Remazeilles Yoel Rephaeli Dominik Riechers Felipe Rojas Aditya Rotti Anirban Roy Sharon Sadeh Yuki Sakurai Maria Salatino Mayuri Sathyanarayana Rao Lauren Saunders Emmanuel Schaan Marcel Schmittfull Neelima Sehgal Joseph Seibert Uros Seljak Paul Shellard Blake Sherwin Meir Shimon Carlos Sierra Jonathan Sievers Cristobal Sifon Precious Sikhosana Maximiliano Silva-Feaver Sara M. Simon Adrian Sinclair Kendrick Smith Wuhyun Sohn Rita Sonka David Spergel Jacob Spisak Suzanne T. Staggs George Stein Jason R. Stevens Radek Stompor Aritoki Suzuki Osamu Tajima Satoru Takakura Grant Teply Daniel B. Thomas Ben Thorne Robert Thornton Hy Trac Jesse Treu Calvin Tsai Carole Tucker Joel Ullom Sunny Vagnozzi Alexander van Engelen Jeff Van Lanen Daniel D. Van Winkle Eve M. Vavagiakis Clara Vergès Michael Vissers Kasey Wagoner Samantha Walker Yuhan Wang Jon Ward Ben Westbrook Nathan Whitehorn Jason Williams Joel Williams Edward Wollack Zhilei Xu Siavash Yasini Edward Young Byeonghee Yu Cyndia Yu Fernando Zago Mario Zannoni Hezi Zhang Kaiwen Zheng Ningfeng Zhu Andrea Zonca

Starting from the $C_{\lambda}$-extended oscillator algebras, we obtain a new deformed $w_{\infty}$-algebra. More precisely, we show that the $C_{\lambda}$-extended $w_{\infty}$-algebra generators may be expressed via the annihilation and creation operators of the $C_{\lambda}$-extended oscillator algebras $a$ and $a^{\dagger}$ as an infinite-dimensional extension of the realization of $sp(2)$ algebra.

J. Douari H. El Kinani

A realization of various algebraic structures in terms of the $C_{\lambda}$-extended oscillator algebras is introduced. In particular, the $C_{\lambda}$-extended oscillator algebras realization of Fairlie-Fletcher-Zachos (FFZ)algebra is given. This latter lead easily to the realization of the quantum $U_t(sl(2))$ algebra. The new deformed Virasoro algebra is also presented.

E. H. El Kinani

In this paper we construct the quantum Virasoro algebra ${\mathcal{L}}_{c}$ generators in terms of operators of the generalized Clifford algebras $C_{n}^{k}$. Precisely, we show that ${\mathcal{L}}_{c}$ can be embedded into generalized Clifford algebras.

E. H. El Kinani

For some countable discrete torsion Abelian groups we give examples of their finite measure-preserving actions which have simple spectrum and no approximate transitivity property.

E. H. El Abdalaoui M. Lemanczyk

We formulate and prove a necessary condition for a sequence of analytic trigonometric polynomials with real non-negative coefficients to be flat a.e.

e. H. el Abdalaoui M. G. Nadkarni

Connection of flat polynomials with some spectral questions in ergodic theory is discussed. A necessary condition for a sequence of polynomials of the type $\frac{1}{\sqrt{N}} \big(1 +\sum_{j=1}^{N-1} z^{n_j}\big)$ to be flat in almost everywhere sense is given, which contrasts with a similar necessary condition for a sequence of polynomials to be ultraflat.

e. H. el Abdalaoui M. G. Nadkarni

In this paper, the invariant subspace method is applied to the time fractional modified Kuramoto-Sivashinsky partial differential equation. The obtained reduced system of nonlinear ordinary fractional equations is solved by the Laplace transform method and with using of some useful properties of Mittag-Leffler function. Then, some exact solutions of the time fractional nonlinear studied equation are found.

A. Ouhadan E. H. El Kinani

The El Ni\~no Southern Oscillation (ENSO) is the strongest driver of year-to-year variations of the global climate and can lead to extreme weather conditions and disasters in various regions around the world. Here, we review two different approaches for the early forecast of El Ni\~no that we have developed recently: the climate network-based approach allows forecasting the onset of an El Ni\~no event about 1 year ahead, while the complexity-based approach allows additionally to estimate the magnitude of an upcoming El Ni\~no event in the calendar year before. For 2023, both approaches predict the onset of an El Ni\~no event, with a combined onset probability of about 89%. The complexity-based approach predicts a moderate-to-strong El Ni\~no with a magnitude of $1.49\pm0.37${\deg}C. Since El Ni\~no events temporarily increase the global temperature, we expect that the coming El Ni\~no will increase the global temperature by about +0.2{\deg}C, likely making 2024 the hottest year since the beginning of instrumental observations. It is possible that as a consequence of this El Ni\~no, the +1.5{\deg}C target (compared to pre-industrial levels) will be temporarily breached already in 2024.

J. Ludescher J. Meng J. Fan A. Bunde H. J. Schellnhuber

The fractional supersymmetry in the case of the non-relativistic motion of one anyon with fractional spin is realized. Thus the associated Hamiltonian is discussed.

J. Douari El H. El Kinani