Este livro foi preparado com carinho e admiração em homenagem a Alexander Plakhov, cuja trajetória científica, generosidade intelectual e calor humano deixaram marcas profundas em todos aqueles que tiveram o privilégio de o conhecer.
A organização e edição desta coletânea ficaram a cargo da Comissão Organizadora do Workshop on Optimization, Dynamics and Convex Analysis, WODCA 2025, que reuniu depoimentos, textos e lembranças com o objetivo de celebrar a vida e a inestimável contribuição de Alexander para a nossa comunidade
Os textos e mensagens aqui reunidos foram escritos por colegas e amigos pessoas que partilharam com ele momentos de trabalho, amizade e inspiração. A diversidade destas vozes reflete a amplitude do seu impacto e o carinho que despertou em todos nós
A capa é da autoria de Celso Assunção O projeto gráfico e a paginação estiveram a cargo de Paula Carvalho, que procurou traduzir o espírito desta homenagem em forma e imagem. A revisão foi de Tatiana Tchemisova
Agradecemos a todos os que contribuíram com palavras, ideias e presença, ajudando a construir este tributo afetuoso a um colega inesquecível.
This book was prepared with affection and admiration as a tribute to Alexander Plakhov, whose scientific career, intellectual generosity and human warmth left a deep mark on all those who had the privilege of knowing him
This collection was organized and edited by Organizing Committee of the Workshop on Optimization, Dynamics and Convex Analysis, WODCA 2025, which brought together testimonies, texts and memories with the aim of celebrating Alexander's life and invaluable contribution to our community
The texts and messages gathered here were written by colleagues and friends - people who shared moments of work, friendship and inspiration with him The diversity of these voices reflects the breadth of his impact and the affection he aroused in all of us
The cover was designed by Celso Assunção Paula Carvalho was responsible for the graphic design and layout, seeking to translate the spirit of this tribute into form and image Tatiana Tchemisova was responsible for the proofreading
We would like to thank everyone who contributed their words, ideas and presence, helping to build this affectionate tribute to an unforgettable colleague
Laudatio for Alexander Plakhov
Professor Alexander Plakhov was born in Moscow, USSR, in 1960 He graduated from Moscow State University in 1981, and in 1986, at the age of 26, he defended his Ph D thesis at the same institution, with a dissertation entitled “Scattering mapping of classical Hamiltonian systems”.
In 2006, Alexander Plakhov obtained the Habilitation from the University of Aveiro, Portugal, and in 2011, he was awarded the Doctor of Science degree by Moscow State University. The title of his dissertation is “Mathematical problems of Newtonian aerodynamics ”
Alexander’s scientific career began at the Institute of Physics and Technology in Moscow, where he worked from 1984 to 1996, progressing from Junior Researcher to Senior Researcher. In 1996, he was appointed Associate Professor at the Moscow State Technical University
That same year marked the beginning of his international academic journey Having been awarded a NATO Research Fellowship, he moved to Portugal to work at INESC (Institute for Systems Engineering and Computers) in Lisbon From 1997 to 1998, he was an Invited Professor at UENF (Universidade Estadual do Norte Fluminense) in Campos-RJ, Brazil.
In 1999, Professor Plakhov joined the University of Aveiro, where he has been working ever since in the Department of Mathematics initially as an Invited Associate Professor, and currently as an Associate Professor. While maintaining this position, he worked in Aberystwyth University (UK) as a research lecturer from 2007 to 2009.
Alongside his position in Portugal, since 2011, he has served as a Senior Researcher at CIDMA (Center for Research and Development in Mathematics and Applications) of the University of Aveiro, where since 2018 he coordinates the Optimization, Graph Theory and Combinatorics Group.
The research interests of Alexander Plakhov focus on dynamical systems and optimization One of the characteristics of his research is its interdisciplinarity: many of his important results are at the intersection of Newton’s problem of minimal resistance with theories of billiards, optimal mass transport, Kakeya problem, and classical geometry This research has found interesting and unexpected applications in geometric optics; the discovery of various kinds of invisible bodies and retroreflectors should be mentioned In mechanics, the Magnus effect for spinning bodies in highly rarefied media has been studied.
Alexander Plakhov has been the recipient of numerous awards and research grants, including funding from the Moscow State University, the Leading Scientific School in Mathematics, Russia, the FCT – Fundação para a Ciência e a Tecnologia (Portugal), and the Royal Society (International Exchanges Programme, UK).
He was the principal investigator and coordinator of two FCT-funded research projects: in 2007–2010: Optimization of Newtonian resistance for non-convex bodies (PTDC/MAT/72840/2006), in 2011–2013: Scattering of billiards and applications to aerodynamics of rarefied media (PTDC/MAT/113470/2009), and, in 2016–2018, together with Prof Alexey Piunovskiy, he co-supervised the Portuguese-British research project “Constrained impulsive optimal control” of the Royal Society of International Exchanges of UK
Professor Plakhov has authored and edited three books, including a scientific monograph entitled Exterior billiards Systems with impacts outside bounded domains. (Springer, New York, 2012), a didactic volume for a course in Differential Equations edited in 2019, and an edited collection of revised selected works from the 30th EURO Mini-Conference “Optimization in the Natural Sciences”, which he co-chaired in Aveiro, February 2014
Alexander has published more than 80 peer-reviewed articles in scientific journals and conference proceedings. His network of collaborators includes approximately 30 co-authors from 10 countries, and he has carried out numerous research visits to prestigious universities and laboratories worldwide
As a dedicated educator, Professor Plakhov has taught a wide range of courses at both bachelor’s, master’s, and PhD levels, supervised several master's theses, advised three Ph D students, and mentored multiple postdoctoral fellows.
He supervised the PhD of Paulo Gouveia, Pedro Cruz, Alena Aleksenko and post-doctoral research of Evgeny Lakshtanov, Sergey Kryzhevich, Ivan Beschastnyi, and Alena Aleksenko
In his research, he fruitfully collaborated with Pedro Cruz, Evgeny Lakshtanov, Tatiana Tchemisova, Delfim Torres, Victor Neves (Aveiro), Arseniy Akopyan (Vienna), Alexey Davydov (Moscow), Paulo Gouveia (Bragança), Sergey Kryzhevich (Gdansk), Gennady Mishuris (Aberystwyth), Alexey Piunovskiy (Liverpool), Vladimir Protasov (L’Aquila), Vera Roshchina (Sydney), Sergey Tabachnikov (Penn State).
Professor Alexander Plakhov has made outstanding and widely recognized contributions to mathematics, particularly in the fields of geometric optics, optimal mass transport, and the calculus of variations His research is marked by exceptional originality and mathematical depth, with applications that bridge pure theory and applied physics.
Throughout his career, Professor Plakhov has demonstrated a remarkable ability to translate physical intuition into rigorous mathematical models, solving longstanding open problems and opening new directions of inquiry. His contributions are not only technically profound but also conceptually elegant, influencing a broad spectrum of disciplines, from mathematical physics and control theory to geometric analysis
One of his most influential areas of work lies in the problem of least aerodynamic resistance, where he investigated Newton-type problems involving bodies moving through a rarefied medium. Alexander Plakhov made an important contribution to Newton’s problem, which has experienced a new rise since the seminal work by Buttazzo and Kawohl in 1993.
He solved the problem for nonconvex bodies with the use of the theory of billiards: it was shown that the infimum of resistance is zero in reasonable classes of bodies
Several results were connected with Newton’s problem for convex bodies; in particular, it was proved that the surface of an optimal body is developable outside the closure of its singular set The proof is based on a geometric method of small variation of a convex body invented by the author. The study on minimal resistance for slowly rotating bodies with fixed volume led the author to the notion of billiard in domains with rough surface, a notion which was a few years later rediscovered by American mathematicians This study is made with the use of optimal mass transport theory As a by-product of this work, several exact results on optimal mass transport were obtained. It was proved that the mean resistance of a convex body can be reduced, approx., by 1 22% in the 2D case and by 3.05% in the 3D case by roughening its surface. Some other results on slowly and rapidly rotating (or oscillating) bodies, and application to the so-called Magnus effect, were obtained jointly with T. Tchemisova and P. Gouveia
Equally notable is his research on the mathematical theory of invisibility and geometric optics In his seminal monograph "Exterior Billiards: Systems with Impacts Outside Bounded Domains" (Springer, 2012), Professor Plakhov developed a rigorous framework for understanding systems of light and particle reflection outside bounded regions, extending classical billiard theory into new and challenging territory. This work has had a profound impact on the development of invisibility theory in mathematical physics Following this result,
several families of invisible bodies, within geometric optics, were discovered (joint work with V. Roshchina, V. Lakshtanov, and A. Aleksenko).
Another interesting application in geometric optics concerns the creation of retroreflectors, which can be treated as bodies of maximal resistance. Several classes of asymptotically optimal retroreflectors were found A longstanding problem on least resistance in classes of bodies satisfying the oneimpact assumption was solved The solution is based on Besicovich’s method of solving the Kakeya problem, and was honored by publication in the prestigious journal SIAM Review
Recently, billiard dynamics in a rotating half-plane was studied in detail (with S Kryzhevich) Several inequalities between Lp norms of convex functions were established (with V. Protasov), and the obtained results were applied to Newton's problem
Note finally that A Plakhov have works outside his main fields One of them was an incursion into Artificial Neural Networks with paper: "A stochastic approximation algorithm with step-size adaptation" The work influenced posterior improved methods for solving stochastic approximation problems and has been cited in applied works like "Online Robust Subspace Tracking", "Approximate Bayesian Computation", "Calculation of Steady-State Conditions in Thermal Reactors", and others.
Testimonials
CEOC - Center for Studies in Optimization and Control
Domingos Cardoso
Alexander Plakhov received his undergraduate and postgraduate studies at Lomonosov Moscow State University (including his PhD in Mechanics and Mathematics, which he completed in 1986) There, he also served as an Associate Professor (Mathematics) from 1996 to 1997. Afterwards, from 1997 to 1998, he was a NATO research fellow in Lisbon Between 1998 and 1999 he was a Visiting Professor (Mathematics) at the Darcy Ribeiro State University of Northern Fluminense, Rio de Janeiro, Brazil Between 1999 and 2008, he served as a Visiting Associate Professor in the Department of Mathematics of the University of Aveiro (UA).
When Alexander Plakhov arrived to Aveiro in 1999, I was involved in the creation of CEOC – Center for Studies in Optimization and Control, a research center of which I became Coordinator in 2002. I remember his complaints about the hot days in Brazil, which was probably the main reason why he applied for a position in Portugal. I immediately recognized that I was in front of a mathematician of the highest quality who would certainly help us grow scientifically, in particular expanding our research topics to Mathematical Physics.
All these qualities were confirmed throughout all these years in which I had the privilege of counting on his support and collaboration He later got a longterm contract as Auxiliary Professor, between 2008 and 2013, and Associate Professor after 2013, both positions in the Mathematics Department of UA In 2006 he got the Habilitation (Agregação) degree from University of Aveiro. I had the honor of being part of the Qualification Committee and the privilege of observing the excellence of the research he had developed up until then
Alexander Plakhov has been a leading member of the Optimization, Graph Theory and Combinatorics (OGTC) Group since its creation in 2002 as a research group of CEOC He continued as a member of the OGTC Group which became part of CIDMA, the new research unit created in 2010, having assumed the Coordination of this Group since 2018
Esteemed friend Alexander Plakhov, congratulations on your 65th birthday I wish you to continue your successful career among us, always trying to bring together our younger colleagues around your research work as you have always done A huge hug. We'll continue seeing each other around.
Aveiro, June 11, 2025. Domingos Cardoso
Andrey Sarychev
Мы познакомились с Сашей Плаховым в 1999 году, когда он переехал в Авейру. Несмотря на московские корни и не слишком большую разницу в возрасте, познакомиться или хотя бы услышать друг о друге нам до этого не довелось. Годы 1999-2001 были, наверное, последними, когда департамент математики университета Авейру, не объявлял специальных конкурсов на замещение должностей. Нужны были сильные кандидаты с PhD в любых областях математики. К тому моменту я преподавал в департаменте уже 6 лет и был координатором исследовательского центра. Вероятно, в качестве координатора и «эксперта по российским математикам», я и получил от тогдашней директорки департамента пакет с документами и CV, которые Саша Плахов прислал в Авейру из Бразилии, где преподавал в университете одного из приэкваториальных штатов. CV не позволял усомниться в том, что департамент приобретает «ценный кадр». То, что Саша после нескольких семестров, проведенных в Бразилии, как-то владел португальским языком, делало его кадром бесценным. Так мы встретились. Саша, как многие математики и
горным туризмом и бегом. В
переезда в Португалию возраст (40 лет) давал о себе знать, и Саша перешел на полумарафоны.
проходил полумарафон довольно высокого уровня, но со свободной регистрацией участников. Саша и некоторые молодые португальские коллеги зарегистрировались бежать, мы, остальные, пришли поболеть. Саша финишировал 28м или 29м. Я поздравил его с некоторым чувством неловкости. Когда чуть позже награждали тех, кто финишировал первыми, я услышал, что многие из них – призеры мировых первенств.
Я не припомню докладов Саши на научных семинарах по изначальной его тематике – эргодический теории. Возможно, он участвовал в конференциях по динамическим системам, в которых не участвовал я. В департаменте у всех нас была очень большая учебная
черте, нередкой у математиков. По его собственному признанию и по наблюдениям (немногих) близко с ним общавшихся, он человек несколько замкнутый и в основном сосредоточенный на общении в кругу семьи. Тем удивительней его чрезвычайно широкий круг научного сотрудничества, впечатляющее количество соавторов. Я знаю, что многие из них встречаются
Авейру. Желаю интересных докладов, разговоров на математические и нематематические темы, стартов
We met with Sasha Plakhov in 1999, when he moved to Aveiro. Despite his and my Moscow roots and the relatively small age difference between us, we had never met or even heard of each other before.
The years 1999–2001 was probably the last period when the Department of Mathematics in Aveiro did not announce job openings for specific teaching positions. Strong candidates with PhDs in all areas of mathematics were welcome. By that time, I had already been teaching in the department for six years and was the coordinator of the research center. Probably, as the coordinator and the “general expert on Russian mathematicians,” I received from the then head of the department a package of documents and a CV which Sasha Plakhov had sent to Aveiro from Brazil, where he was teaching at a university in the one of the equatorial states. The CV left no doubt that the department was acquiring a “valuable asset.” The fact that Sasha, after spending several semesters in Brazil, could master some Portuguese made him an invaluable asset. That is the way we met.
Sasha, like many mathematicians and physicists around the world, is passionate about mountain tourism and jogging. In his youth, he participated in marathons. By the time he moved to Portugal, his age (40 years) was starting to show, and Sasha switched to half-marathons. Shortly after his arrival in Aveiro, there was a half-marathon of quite a high level, but with open registration for participants. Sasha and some young Portuguese colleagues signed up to run, while the rest of us came to cheer. Sasha finished 28th or 29th and I congratulated him with a bit of embarrassment. At the end, when top winners of the halfmarathon have been awarded, I learned that quite few of them were participants and medalists of the world championships.
I do not recall Sasha’s talks at scientific seminars on his original field of research —the ergodic theory. Perhaps he spoke at some conferences on dynamical systems which I did not attend. At the time all of us had a very heavy teaching load. Besides, Sasha had to take care of his son and his parents, who lived in Russia.
I recall though that once he borrowed from me a book by V.M. Tikhomirov “On maxima and minima”. Few days later, he asked a couple of questions about Newton’s aerodynamic problem, and in a week or two he mentioned that he has an idea for changing the formulation of this problem —abandoning the assumptions of convexity, monotonicity of the profile, and the hypothesis of uniqueness of particle collisions. In 2003, when I was already working in Florence, Plakhov has visited Scuola Normale Superiore of the University of Pisa with seminars on application of billiard techniques to studying Newton’s problem and similar ones. Over the past 20+ years, Sasha has developed this topic deeply and broadly and undoubtedly remains leading expert to this day.
Finally, I just want to touch on one of Sasha's personal and professional traits, which is not uncommon among mathematicians. By his own admission and according to few people who know him well, he tends to be a bit reserved. His family circle is where he spends most of his time. It is impressive though how wide is his network of scientific collaborators and coauthors around the globe, how outgoing he is in establishing new scientific contacts .
I know that many of the collaborators will meet this June at the Department of Mathematics of the University of Aveiro at a conference dedicated to Sasha Plakhov’s 65th birthday. I wish for interesting talks, conversations on both mathematical and non-mathematical topics, and the beginnings of fruitful collaborations. Wishing you a successful, long, and productive life, Sasha! Happy Birthday!
Delfim Torres
Do Colega e Amigo Alexandre Plakhov muito podia dizer: orientámos um aluno de doutoramento em conjunto, o Paulo Gouveia, que defendeu o seu doutoramento na Universidade de Aveiro em 2008; somos co-autores em 8 artigos de investigação; participámos conjuntamente em pelo menos 3 projetos de investigação; organizámos e participámos em várias conferências; etc. Mas não vou falar aqui de matemática, vou falar de um dos passatempos que nos une: a corrida.
Comecei a correr em dezembro de 2000, ainda aluno de doutoramento, motivado após ter visto o Plakhov a terminar uma meia-maratona na cidade de Aveiro. Devo sem dúvida o bichinho da corrida ao Plakhov. Obrigado bom amigo. Muito provavelmente se não fosses tu nunca teria feito uma meia-maratona na vida e são já 32 as que fiz, não esquecendo as 7 maratonas, sempre inspirado pelo facto de teres tu corrido 12 maratonas!
A primeira vez que corri com o Plakhov foi em 13 de janeiro de 2001: demos três voltas juntos à Universidade, num ritmo calmo, cobrindo 9Km em aproximadamente 60 minutos. Na semana seguinte, a 20 de janeiro, corremos novamente juntos os mesmos 9Km, dessa vez também com o colega João Pedro. A partir daí não mais parei: no dia seguinte, 21 de janeiro de 2001, corremos, eu e o Plakhov, mais 12Km e, no mês seguinte, em fevereiro de 2001, já corríamos juntos 28Km em 2h20m (ao ritmo de 5m00s por Km). As competições foram também surgindo naturalmente, a primeira de longa distância a 11 de novembro de 2001 em que fizemos juntos a 27ª meia-maratona da Nazaré (a minha primeira meia-maratona!): eu com 30 anos de idade completei os 21,1Km em 1h26m, o Plakhov com 41 anos em 1h25m (eu bem tentei, mas o sénior não conseguiu apanhar o veterano...).
Muitas outras meias-maratonas se seguiram, menciono aqui apenas duas em que consegui ficar à frente do Plakhov: a 3ª meia-maratona de Esposende, realizada a 7 de abril de 2002, onde terminei em 1h30m e o Plakhov em 1h33m; e a 28ª meia-maratona de Ovar, realizada a 2 de outubro de 2016, onde eu corri como Veterano M45 e terminei em 1h40m, e o Plakhov correu como Veterano M55 em 1h46m. Mas em abono da verdade, devo dizer que, não obstante ser 11 ou 12 anos mais novo que o Plakhov, a maior parte das vezes cortei a meta atrás do meu amigo, mesmo nas provas mais curtas de 10Km em que participámos: por exemplo no 20º Grande Prémio de Atletismo "Os Ílhavos", a 16 de fevereiro de 2003; no 18º Grande Prémio de Atletismo de Estarreja, a 23 de fevereiro de 2003; a 8 de novembro de 2015 em Albergaria-a-Velha, onde o Plakhov terminou os 10Km em 51 minutos e eu em 54; ou na Corrida Cidade Aveiro, a 3 de abril
de 2016, onde eu corri os 10Km ao ritmo de 4m39s por Km e o Plakhov a mesma distância ao ritmo de 4m30s por Km, não obstante eu correr como Veterano M40 e o Plakhov como Veterano M55...
Bons corredores? Com certeza que não, pois de prémios apenas me lembro de um, em equipa com o João Pedro: a 5 de novembro de 2002 participámos na 2ª Corrida do Caloiro da UA (prova de 3Km organizada pelos estudantes), onde a "Equipa Matemática", formada por Plakhov, Delfim e João Pedro, conseguiram um terceiro lugar, premiado por um troféu que oferecemos ao DMat e se encontra na Sala dos Professores (ver foto).
O importante são mesmo os Km partilhados, as muitas conversas durante as corridas e as lições que aprendemos: que a vida deve ser simples e que, quer estejamos a correr uma maratona ou apenas a fazer uma corrida de 20 minutos, o que realmente interessa é estar presente, colocar um pé à frente do outro, começar, fazer o trabalho, dividir os objetivos em passos mais pequenos, possíveis, e continuar a dar esses passos até chegarmos onde queremos estar. É isso que fazemos na corrida, é isso que fazemos na matemática e na vida.
Parabéns pelo teu sexagésimo quinto aniversário, desejo-te as maiores felicidades e muitos mais milhares de Km, Delfim (Aveiro, 3 de junho de 2025)
I could say a lot about my colleague and friend Alexander Plakhov: we co-supervised a PhD student, Paulo Gouveia, who defended his thesis at the University of Aveiro in 2008; we are co-authors of 8 research papers; we have participated together in at least 3 research projects; we have organized and taken part in several conferences; etc. But I am not going to talk about mathematics here — I am going to talk about one of the hobbies that brings us together: running.
I started running in December 2000, still a PhD student at the time, motivated after seeing Plakhov finish a half marathon in the city of Aveiro. Without a doubt, I owe my love for running to Plakhov. Thank you, my good friend. Most likely, if it weren’t you, I would never have run a half marathon in my life — and I have now done 32 of them, not to mention 7 full marathons, always inspired by the fact that you have run 12 marathons yourself!
The first time I ran with Plakhov was on January 13, 2001: we did three laps around the University together, at a relaxed pace, covering 9 km in approximately 60 minutes. The following week, on January 20, we ran the same 9 km together again, this time also joined by our colleague João Pedro. From that point on, I never stopped: the very next day, January 21, 2001, Plakhov and I ran another 12 km, and the following month, in February 2001, we were already running 28 km together in 2h20m (at a pace of 5m00s per km). Races also started coming naturally, the first long-distance one being on November 11, 2001, when we ran the 27th Nazaré Half Marathon together (my first half marathon!): I was 30 years old and completed the 21.1 km in 1h26m, while Plakhov, at 41 years old, did it in 1h25m (I really tried, but the senior could not quite catch the veteran...).
Many other half marathons followed, and I will mention here just two in which I managed to finish ahead of Plakhov: the 3rd Esposende Half Marathon, held on April 7, 2002, where I finished in 1h30m and Plakhov in 1h33m; and the 28th Ovar Half Marathon, held on October 2, 2016, where I ran as a Veteran
M45 and finished in 1h40m, while Plakhov ran as a Veteran M55 and finished in 1h46m. But in all fairness, I must say that, despite being 11 or 12 years younger than Plakhov, most of the time I crossed the finish line behind my friend, even in the shorter 10 km races we took part in — for example, in the 20th "Os Ílhavos" Grand Athletics Prize on February 16, 2003; the 18th Estarreja Grand Athletics Prize on February 23, 2003; on November 8, 2015 in Albergaria-a-Velha, where Plakhov finished the 10 km in 51 minutes and I in 54; or at the Aveiro City Run on April 3, 2016, where I ran the 10 km at a pace of 4m39s per km and Plakhov ran the same distance at a pace of 4m30s per km — even though I was running as a Veteran M40 and Plakhov as a Veteran M55...
Good runners? Certainly not, as I can only remember one prize, and that was as a team with João Pedro: on November 5, 2002, we took part in the 2nd UA Freshman Run (a 3 km race organized by students), where the “Mathematics Team,” made up of Plakhov, Delfim, and João Pedro, managed to take third place — awarded with a trophy that we donated to the Department of Mathematics and which is now in the “Sala dos Professores” (see photo).
What truly matters are the kilometers shared, the many conversations during the runs, and the lessons we have learned: that life should be simple, and whether we are running a marathon or just doing a 20-minute run, what really matters is showing up, putting one foot in front of the other, getting started, doing the work, breaking down our goals into smaller, achievable steps, and continuing to take those steps until we reach where we want to be. That is what we do in running, that is what we do in mathematics, and that is what we do in life.
Happy sixty-fifth birthday! I wish you all the best and many more thousands of kilometers, Delfim (Aveiro, June 3, 2025)
Giuseppe Buttazzo
A few photos from Alexander’s Agregação ceremony I had the honor of serving as a sort of mentor during the event In this role, while the candidate (Alexander) was responsible for presenting only his personal and academic background, it was up to me to deliver the scientific presentation, highlighting and contextualizing his most significant contributions to the field. Thankfully, everything proceeded smoothly, and the verdict, symbolized by the colored balls placed in the respective boxes, was unanimously favorable.
Happy birthday, Alexander!
Giuseppe
Tatiana Themisova
ДорогойСаша, сДнёмРождения! Моя история в Университете Авейру тесно связана с твоeй Мы началиработатьводинитотжеучебныйгод, втечениенескольких лет делили один кабинет, читали лекции одному и тому же потоку студентов Calculus, вместе распивали чай и вели долгие беседы о жизни, о математике, о детях, о книгах, и о политике тоже Спорили нонессорились, хотяячастопсихуюатыиногдаупрям...
Знаю что любишь хорошие стихи, и надеюсь что тебе много стихов прочлиипосвятили, чтотыконечнозаслуживаешь А я просто попробую вспомнить и проиллюстрировать, с чем ассоциируется у
Dear Sasha, Happy Birthday!
My story at the University of Aveiro is closely linked to yours We started working in the same academic year, shared the same office for several years, lectured to the same cohort of Calculus students, took our tea together, and had long conversations about life, math, children, books, and politics, too. We argued, but did not quarrel, although I often freak out, and you are sometimes stubborn...
I know that you love good poems, and I hope that many verses have been read to you and dedicated, which you certainly deserve And I will just try to remember and illustrate what I associate your name and your image with, and why you are a very important friend and comrade for me, whose opinion is very important to me, and on whom I can always count and who will always respond and support.
Time flies quickly, but the fame of your constructions spreads even faster. That’s why I got to know them before I got to know you
I'm very glad that our brief conversation about the single-impact problem later turned into an article, and now I consider myself a co-author of a classic.
Thanks to you, Aveiro is the first city that comes to my mind when I think of Portugal
I wish you to find the unfound, construct the unconstructed, and prove the unproven!
Arseniy
Alexey Davydov
Feliz 65º aniversário! Saúde e boa sorte!
Спортсмен-бегун и математик,
Активный в жизни человек, с
Широким умным горным взглядом, Ему преград по жизни нет!
Sportsman and mathematician,
Activities from ancient dreams, and Seconds are for measure funs,
Creation for formulas and sums, while Holidays are not at all,
And lucky life with works and wife.
Alexey Davydov, Vladimir – Moscow, 2025
Evgeny Lakshtanov
In late autumn 2004, when my PhD dissertation was nearing its final stage, I received a call in my room on the 16th floor of Zone B of the main building of Moscow State University. It was my official supervisor on the line, telling me that his former student, Alexander Yuryevich Plakhov, was looking for an assistant to work on the wave analogue of some mechanical problem. That was the first time I heard about Sasha, and that meeting would go on to shape both my children’s childhood and my scientific interests for many years to come.
I remember how, around that time, I first looked up Portugal on Yandex Maps and could hardly imagine myself living by the ocean Dima Yarodsky, my senior colleague and also a student of Minlos, though by then already a former postdoc, told me all sorts of horror stories about how supervisors exploit postdocs and how dependent postdocs are on them, and so on These stories certainly made an impression on me. But I liked both Sasha and Aveiro from the start. Over these 18 years, Sasha has always offered every possible support to me and Alena Sasha, huge thanks to you!
João Pedro Cruz
Obrigado Plakhov! Com gosto faço parte desta celebração
No distante início, nesta terra junto à ria, aproximaste-te, estocasticamente, ao que eu matematicamente conhecia Deu os seus frutos com algumas citações Porém, depois seguimos rumos diferentes, até um novo reencontro em construção. Tudo sempre com um computador por perto
Pelo caminho, fomos até Vigo, em divertida jornada social com os colegas do DMat, e com toda essa energia, além das mariscadas, ainda deu tempo para uma matinal corrida num dos parques da cidade frente ao rio ou ria
Mais tarde, sugeriste uma visita a Aberystwyth (“boca do rio Ystwyth”), cidade novamente rodeada de água como Aveiro O mar e os verdejantes montes sempre inspiram para umas longas jornadas de simulações, sempre com o computador atrás Nunca partilhei mas aí converti-me, ainda que por um ano, ao vegetarianismo ao ver as simpáticas ovelhinhas nos montes da zona
Entire life, with great persistence, You search for minimal resistance.
Luís Descalço
Ao longo dos vários anos em que trabalhei com o Plakhov, o que mais me marcou além do seu notável talento para a Matemática foi a sua humildade e bondade
Lembro-me de inúmeros momentos em que ambos nos comovíamos simplesmente pela alegria de ajudar e de ser ajudado.
Sempre de acordo com tudo, cada interação terminava com sorrisos genuínos.
Desejo tudo de bom a este querido colega e amigo
Manuela Souto de Miranda
Dear Alexander Plakhov,
It is a pleasure to have the opportunity to participate in this tribute with a few words. I couldn’t find any picture, nor signed documents that could state our relationship. But I have memories: I remember my functions at the Department in 1999; how I believed that your contract with University of Aveiro would be a previously won scientific challenger, and how it would represent an added value to our research centre. After some years, we restate that the Department invited and incorporated a person worth knowing as a colleague, as a committed teacher and as an excellent researcher. I am proud with my contribution to the process and, mostly, to your stay with us.
Kind regards,
Paula Carvalho
Parabéns pelos seus 65 anos!
É uma honra dividir o corredor com um cientista tão brilhante, sempre generoso e afável Muito obrigada pela sua constante gentileza e disponibilidade
Desejo que esta nova etapa lhe traga tanta inspiração quanto a que sempre nos ofereceu!
Generated with AI Tools, by Paula Carvalho
Rute Lemos
Caro Plahkov,
É com muito gosto que apresento as minhas felicitações pelo aniversário, mas também pelo percurso científico
Lembro-me do tempo em que partilhámos gabinete, junto com a Tatiana, e no primeiro Dia da Mulher, nos surpreendeu a ambas com uma flor para o celebrar, o que à data era ainda pouco usual em Portugal.
Muito obrigada pela cordialidade, serenidade e boa disposição que sempre alicerçaram a sua forma de estar na vida
Desde cedo, recordo as palavras do Prof Domingos sobre a qualidade dos seus trabalhos de investigação e, mais recentemente, os contributos para o divulgar a públicos mais jovens, na Academia de Verão, com o tema da geometria da indivisibilidade Enquanto responsável científico do OTGC, agradeço ainda a forma como sempre incentivou a concretização dos nossos planos
Que possa manter o Desporto, ao lado da Matemática, por tanto tempo quanto desejar!
