Department of Mathematics and Systems Analysis

Current

Defence of doctoral thesis in the field of mathematics, Msc Joona Karjalainen, 17.12.2021

19. November 2021
Title of the doctoral thesis is "Structure and estimation of network models with overlapping communities"


Opponent is Professor Remco van der Hofstad, Eindhoven university of technology, The Netherlands

Custos is Professor Lasse Leskelä, Aalto University School of Science, Department of Mathematics and Systems Analysis

The public defence will be organised on campus.

The doctoral thesis is publicly displayed 10 days before the defence in the publication archive Aaltodoc of Aalto University.

Electronic thesis (link will be added)


Defence of doctoral thesis in the field of mathematics, LicSc (Tech) Diana Andrei, 10.12.2021

19. November 2021

Title of the doctoral thesis is "Extensions of the multicentric functional calculus"

Opponent is Doctor Jani Taskinen, University of Helsinki, Finland

Custos is Professor Juha KinnunenAalto University School of Science, Department of Mathematics and Systems Analysis

The public defence will be organised on campus.

The doctoral thesis is publicly displayed 10 days before the defence in the publication archive Aaltodoc of Aalto University.

Electronic thesis (link will be added)


Defence of doctoral thesis in the field of Systems and Operations Research, M.Soc.Sc. Jussi Lindgren, 17.12.2021

19. November 2021
Title of the doctoral thesis is "The Principle of Least Action and Stochastic Dynamic Optimal Control - Applications to Economic, Financial and Physical Systems"

Opponent is Professor Grigorios A. Pavliotis, Imperial College London, UK

Custos is Professor Ahti Salo, Aalto University School of Science, Department of Mathematics and Systems Analysis

The public defence will be organised via Zoom and on campus. Link to the event will be added

Zoom Quick Guide

The doctoral thesis is publicly displayed 10 days before the defence in the publication archive Aaltodoc of Aalto University.

Electronic thesis (will be added)



Postdoctoral Researchers in the general area of Mathematical Physics / Random Geometry / Conformal Field Theory

17. November 2021

The Department of Mathematics and Systems Analysis (http://math.aalto.fi/en/) is seeking 2-3

Postdoctoral Researchers in the general area of Mathematical Physics / Random Geometry / Conformal Field Theory

to work in the research groups of Profs. Eveliina Peltola and Kalle Kytölä. The positions are offered for 2(+1) years, starting between January and October 2022.

The review of applications will begin on December 1st, 2021 (first deadline), and the selection may be done also before the final deadline December 31st, 2021.


Doctoral candidate positions in Mathematics, Operations Research and Statistics

17. November 2021

The Department of Mathematics and Systems Analysis (https://math.aalto.fi/en/) at the Aalto School of Science is seeking several

Doctoral Candidates in Mathematics, Operations Research and Statistics

The candidates will work within one of the department’s main research areas

  • Algebra and discrete mathematics,

  • Analysis and partial differential equations,

  • Numerical analysis,

  • Stochastics, statistics and mathematical physics,

  • Systems and operations research.

The review of applications will begin on 15 December 2021 (first deadline), and decisions may be made already before the final deadline on 16 January 2022 at 23:59 EET (UTC+2).


Postdoctoral Researcher in Algebraic Statistics

17. November 2021

The Department of Mathematics and Systems Analysis (http://math.aalto.fi/en/) at the School of Science is seeking a

Postdoctoral Researcher in Algebraic Statistics

The postdoctoral researcher will work in the research group of Kaie Kubjas. The position is part of the Academy of Finland project “Algebraic geometry of hidden variable models in statistics”. The position is for one year with the starting date on September 1st, 2022.

To guarantee full consideration, the application should be received by December 15, 2021.

New hourly paid teachers of mathematics and systems analysis for spring 2022

19. October 2021

The Department of Mathematics and Systems Analysis is seeking

New hourly-paid teachers in Mathematics and Systems Analysis for spring term 2022.

Your tasks include teaching in exercise groups and grading exercises and exams.

Regarding teaching in mathematics, we expect the applicants to have completed at least 20 credits of mathematical studies at university level with good grades. Regarding teaching in systems analysis (courses MS-C/E2xxx), we expect the applicants to have completed the course they are interested in. If you have previous experience in teaching, it is considered as an advantage, but is not necessary. This is a part-time job (2-4 hours/week). The salary is 30-40 euros/teaching hour based on your education level.

Grading exercises and exams will be (typically) compensated separately (300-400 euros depending on your education and the course level).

Read carefully! If you are not working for Aalto at the moment you apply, fill in the application form here. If you are working for Aalto at the moment you apply, you have to apply as an internal candidate via Workday, see instructions Sisäisen työpaikan hakeminen | Aalto-yliopisto.

Attach an open motivation letter, a cv and a transcript of records as one PDF file.

Deadline for the applications is Monday 8 November 2021.

Based on the applications, we will invite some of the applicants for a web interview.

More information: johanna.glader@aalto.fi 

More information:

johanna.glader(at)aalto.fi

Note: if you have previously worked as an hourly-based teacher at the MS Department, you will receive a separate link from johanna.glader(at)aalto.fi. 

 

 


Defence of doctoral thesis in the field of mathematics, M.Sc. Valentina Candiani, 12.11.2021

28. September 2021

Medical imaging refers to several different techniques that are used to image the interior of a human body based on exterior measurements in order to diagnose, monitor and treat medical conditions. This dissertation is aimed at understanding how Electrical Impedance Tomography can be valuable as a noninvasive medical imaging modality, in particular for its application to the detection and classification of stroke.

The objective of Electrical Impedance Tomography is to reconstruct information on the conductivity distribution inside the examined physical body from boundary measurements of currents and voltages. Due to the distinct conductivity levels of different tissues, mapping the internal conductivity of a human body allows one to, e.g., detect possible anomalies.

Mathematically, the associated inverse problem presents several theoretical and numerical challenges, and, in real-life applications, measurement and modelling errors considerably deteriorate the available data. The purpose of the research at hand is to develop algorithms and methods for handling such realistic measurement settings.

To this end, a novel computational three-dimensional head model is introduced and utilized to simulate realistic synthetic measurements on a finite number of contact electrodes. The examined solution strategies for the inverse problem correspond to different methodologies, ranging from regularized iterative reconstruction algorithms to machine learning techniques. The performance of the developed methods is assessed via three-dimensional simulated experiments.

Opponent is Professor Erkki Somersalo, Case Western Reserve University, USA

Custos is Professor Nuutti Hyvönen, Aalto University School of Science, Department of Mathematics and Systems Analysis

Contact details of the doctoral student: valentina.candiani@aalto.fi

The public defence will be organised via Zoom and on campus. Link to the event

Zoom Quick Guide

The doctoral thesis is publicly displayed 10 days before the defence in the publication archive Aaltodoc of Aalto University.

Electronic thesis


Defence of doctoral thesis in the field of industrial engineering and management, MSc Juha Törmänen, 16.9.2021

30. August 2021

Today's remote and hybrid work focused environment places new pressures on the well-being and success of both organisations and employees. Systems Intelligence, meaning intelligent behaviour in the context of complex systems involving interaction and feedback, can help the well-being and improvement of teams and individuals even in these challenging conditions. Systems Intelligence has been researched in the Aalto University Systems Intelligence Research Group since the early years of the 2000s, led by Raimo P. Hämäläinen and Esa Saarinen.

This dissertation provides new tools for measuring and illustrating Systems Intelligence. The study introduces the eight factors of Systems Intelligence – Systemic Perception, Attunement, Positive Attitude, Spirited Discovery, Reflection, Wise Action, Positive Engagement and Effective Responsiveness – and demonstrates that these factors can be assessed with self, peer, and organizational evaluations. Additionally, the study introduces the PoSITeams simulation tool that helps people explore socio-emotional systems.

The results of the research show that companies and employees who are seen as successful and high performing are also perceived to be strong in the eight factors of Systems Intelligence. Thus, the concepts of Systems Intelligence can help to articulate and highlight success factors that might otherwise remain overlooked in the workplace. The new measurement tools allow assessing and developing these factors at the individual, team, and organisational levels.

These new methods of measuring and modelling Systems Intelligence are especially useful for developing learning organizations and human resources. Organizational learning has often been developed from a top-down leadership viewpoint and by focusing on improving organizational structures. The methods of Systems Intelligence provide a way to conduct development work also from the grassroots level, focusing on the ways and styles people live their daily lives, and by offering concrete improvement suggestions for one's own behaviour.

Opponent: Associate Professor Doctor Hong Bui, University of Bath, United Kingdom

Custos: Professor Esa Saarinen, Aalto University School of Science, Department of Industrial Engineering and Management

Contact information of the doctoral student: juha.tormanen@aalto.fi

The public defence will be organised via Zoom. Link to the event

Zoom Quick Guide

The dissertation is publicly displayed 10 days before the defence in the publication archive Aaltodoc of Aalto University

Electronic dissertation (can be read about 12 days prior the defence)


Defence of doctoral thesis in the field of systems and operations research, M.Sc. Edoardo Tosoni, 14.9.2021

30. August 2021

This dissertation develops probabilistic methodologies for strengthening the systematization of scenario analysis for the safety assessment of nuclear waste management facilities. From the perspective of the Finnish and European nuclear waste community, it contains novel results as, traditionally, this community has only relied on non-probabilistic what-if scenarios. The dissertation also addresses two classical objections to probabilistic approaches. First, the difficulty of obtaining information about the scenario probabilities is tackled by generating data through computer simulations and expert judgments. The quality of these data inputs is characterized by accommodating ranges of probability values, which makes it possible to produce risk estimates even in the presence of scarce information. Moreover, the quantification of uncertainties concerning the residual risk level helps assess the comprehensiveness of the analysis, which, as a goal, cannot be readily attained by non-probabilitstic approaches. Second, the dissertation proposes risk importance measures for identifying which scenarios involve greater risks than others. Thus, these probabilistic methods provide support for structured risk management decisions instead of merely lumping all the data inputs into a single risk estimate. The methodologies are illustrated with case studies on nuclear waste management by examining the spent-fuel storage plant in Saluggia (Italy) and the near-surface repository of Dessel (Belgium). Still, the methodological results are generic as they can be extended to many other application areas, such as finance, in which systemic dependencies must be accounted for. The dissertation has been carried out mainly in the framework of the Finnish research programs KYT 2018 and KYT 2022 on nuclear waste management.

Opponent is Professor doctor Man-Sung Yim, Korea Advanced Institute of Science and Technology, South Korea

Custos is Professor Ahti Salo, Aalto University School of Science, Department of Mathematics and Systems Analysis

The public defence will be organised via Zoom and on campus. Link to the event

Zoom Quick Guide

The doctoral thesis is publicly displayed 10 days before the defence in the publication archive Aaltodoc of Aalto University.

Electronic thesis


Department's summer excusion 2021

19. August 2021
Despite of the stormy wind and some rain, the participants enjoyed the get-together party and the game of Mölkky. See the photos.

Summer 2022 Bridges conference

5. August 2021
In 2022 we are planning to hold an in-person Bridges conference! Join us for invited and contributed talks, hands-on workshops, art galleries and live performance events, and an excursion.

Defence of doctoral thesis in the field of systems and operations research, M.Sc. Juho Andelmin, 23.7.2021

26. July 2021

This dissertation develops new formulations and algorithms for problems in green logistics, centralized resource allocation, and discrete multi-stage stochastic optimization.

Two new algorithms and a formulation are developed for the optimal routing of vehicles whose fuel consumption is monitored to prevent fuel depletion en route. This formulation is especially useful for the routing of electric vehicles. It first computes all refuel paths between each pair of customers with all possible combinations of refueling station visits, then discards those refuel paths that cannot be in the optimal solution, and finally replaces all refueling stations with the remaining refuel paths. This formulation is the first to combine routing and refueling decisions with minimal overhead. An exact algorithm that utilizes a full arsenal of sophisticated optimization techniques is developed, followed by a metaheuristic that computes near-optimal solutions fast and complements the exact algorithm. Both algorithms for serve as building blocks for future problem generalizations. Notably, the average optimality gap of the exact algorithm on 200 - 300 customer instances is about 0.67%.

The centralized resource allocation model computes efficiency scores for a collection (portfolio) of units, such as hospitals or banks, which are controlled by a central decision maker (DM). The model also helps allocate resources to these units so that the efficiency of the portfolio consisting of these units is maximized. Because the units typically have many inputs and outputs, the corresponding optimization problem has multiple objectives. Thus, all non-dominated portfolios satisfying the DM’s preferences are computed and the units’ relative resource ranges over these non-dominated portfolios are visualized. Our results indicate that relying on conventional efficiency scores in guiding resource allocation decisions can cause inefficiencies.

The Decision Programming framework is presented to solve discrete multi-stage decision-making problems arising in stochastic optimization and decision analysis with a novel formulation. It incorporates different types of endogenous uncertainties and risk measures in constraints and/or objective function. The framework offers more flexibility than standard tools in decision analysis, and it has just been adapted to solve a large-scale project portfolio selection problem with uncertain time-dependent returns.

Opponent is Professor M. Grazia Speranza, University of Brescia, Italy

Custos is Professor Ahti Salo, Aalto University School of Science, Department of Mathematics and Systems Analysis

Contact information of the doctoral student: +358403581315, juho.andelmin@aalto.fi


Aalto Mathematics professor wins Outstanding Teacher of the Year from the Finnish Foundation for Technology Promotion's

4. June 2021



Aalto University Professor Fabricio Oliveira, 35, teaches mathematical optimisation to technology students. The aim of this discipline is to optimise a system by using mathematical modelling. This can be used to solve problems like working out the most economical solution for a company, or what actions will have the best environmental impact.

The themes of the courses taught by Oliveira are some of the more difficult themes in system and operations research. However, students praise his way of relating complex, technical themes closely to everyday life: in the course, students learn modelling and optimisation through real-life examples. His interactive and energetic teaching style also generates enthusiasm for the topic among the students. This year was also the first time that the recipient of the Teacher of the Year award was an international technology expert.

‘The exceptional year was also reflected in the nominations for the Outstanding Teacher award. The students commended Fabricio Oliveira for the wonderful ways in which he has succeeded in organising his teaching at a time of remote studying. For many years, international experts have played a big role among the Foundation's grant recipients. It’s wonderful to see that these international recruitments are also positively reflected in teaching,’ says Johanna Lamminen, Chair of the Board of the Finnish Foundation for Technology Promotion.

According to Oliveira, the past year and the Teacher of the Year award provide an excellent opportunity to reflect on what has been successful in teaching and which aspects could still be developed.

‘I believe that, in the future, we can combine the best elements of distance and contact teaching. I’m not going to stop doing lecture videos that allow students to study at their own pace. However, nothing can beat face-to-face encounters — in the lecture hall, I can immediately see on the students' faces if my explanation was not clear, or is missing something,’ Oliveira says.

After having worked in Finland, Brazil, the United States and Australia, Oliveira has noticed some differences in teaching between countries. In Finland students are used to musing on what they have learned in peace, and take more encouragement to join in discussions. On the other hand, the high level of comprehensive school teaching is evident in the lecture halls. ‘Students are students regardless of the country. However, it has been really great to see how high a knowledge level the students have achieved even before their university studies,’ Oliveira says.

Further information:

Professor Fabricio Oliveira, Aalto University
+358 40 489 0080
fabricio.oliveira@aalto.fi

 


Collineation Grounds Exhibition, 26.5 - 26.8.2021

20. May 2021


Event flyer

After successful student exhibitions of the transdisciplinary course Crystal Flowers in Halls of Mirrors: Mathematics meets Art and Architecture in Heureka Science Centre 2017 and Espoo Cultural Centre 2019, Aalto Math&Arts Minor exhibition returns to Otaniemi Campus in spring 2021. During the course, students from diverse disciplines and various stages of their studies have been working together in the realm of mathematics and arts searching interesting structures and concepts to be scrutinized and developed into tangible objects. This work was guided in collaboration with an interdisciplinary team of teachers via lectures, workshops and tutoring sessions.

The theme of the 2021 course highlighted the fundamental role of projective geometry in the development of modern mathematics and interaction with applied fields. Its original growth out of the efforts of architects and painters to present spatial objects on flat surfaces to an exciting branch of mathematics manifests itself in genuine interconnections, that can be developed across metric geometry and further towards other disciplines. From a beautiful and intricate system of consistent propositions about points, lines and planes, a collection of unexpected results follows, stretching our imagination and strengthening the link between mathematics and visual perception. Hand in hand with projective configurations, the exhibition space provides a frame to implement and share ideas and visions about low dimensional geometry and topology, that have been studied in the context of Aalto Math&Arts.

The sheltered courtyard next to the main lobby of the Undergraduate Centre and its dark-red brick, black granite and copper clad façade provides a solid frame for the exhibition. In the spirit of Alvar Aalto, the student works enliven the premises from several perspectives through surrounding windows.

Teachers, Aalto University:

  • Kirsi Peltonen (Responsible Teacher, SCI Mathematics)
  • Taneli Luotoniemi (ARTS Artistic Research)
  • Laura Isoniemi (ARTS Design, Art Education)
  • Günther Filz (ARTS/ENG Architecture)
  • Pauliina Skyttä (Campus Architect, ACRE)
  • Markus Holste (Curator & Exhibition Architect, ARTS)
  • Marco Rodriguez (Curator & Exhibition Architect, ARTS)
  • Luiza Sevele (Curator & Exhibition Architect, ARTS)

 

EMMA

  • Reetta Kalajo, Arja Miller

Kirsi Peltonen: It is strange to go to an abandoned house to meet students via Zoom

18. May 2021
Kirsi Peltonen. Photo: Mikko Raskinen.
Photo: Mikko Raskinen.

How did you become the teacher of the Crystal Flowers in Halls of Mirrors course?

The course Crystal Flowers in Halls of Mirrors: Mathematics meets Art and Architecture started from nothing ten years ago. I teach mathematics at Aalto University's Department of Mathematics and Systems Analysis, and I did not know anyone from the arts or architecture side.

There was a lot of luck on the way. There was a demand for cross-disciplinary, new openings at Aalto University. At the time, Martti Raevaara was the Vice President for Education, and Aalto courses were established. There was nothing new about combining mathematics and art as such, but it had not been presented this systematically before. As a result, an entire minor subject based on this course was born.

I would not have been able to create the course alone. It was important to get people from different fields to commit to it.

What have been the highlights of the course?

My constant source of inspiration is that we have created new connections and a common voice between teachers and students in different fields. There has also been cooperation with museums, such as the Finnish Science Centre, Heureka, and Espoo Museum of Modern Art, EMMA. The museums have participated in the implementation of exhibitions in cooperation with the artists.

A special highlight, however, would be to get the exhibition up and running in these exceptional circumstances. The results of the workshops are abundant, so maybe no one can really prevent the exhibition either. It is now being arranged outside in Otaniemi.

How has daily life been during the corona pandemic in a teacher's perspective?

The Crystal Flowers in Halls of Mirrors course is based on interaction. Attempts have been made to build it, but creating genuine interaction and dialogue while working remotely is really challenging, sometimes even painful. It has required constant adjustments, and plans have had to be changed on the go. I am extremely grateful to the students who have steadfastly bared with us.

Teaching has mainly  taken place online. Small workshops, where students have been divided into different rooms, have been organised in the Design Factory, while some students have participated through a video connection. Organising has been challenging.

The course is very laborious and requires attendance, as well as tolerance of uncertainty. It is handicraft! When everyone is sitting around the same table on a course, it is easier to understand what the other person is talking about. Remote communication causes a lot of misunderstandings, and it is difficult for a third person to join the discussion when the other two have already started.

All students have quite different situations and backgrounds. Nevertheless, they are incredibly adaptable and have the ability to consider different sides and deal with the situations open-mindedly. I believe both students and teachers have started to appreciate face-to-face teaching more. The lack of interaction is uncomfortable and leads to a strange melancholy feeling, and this cannot continue.

What has helped you cope in daily life during the times of Covid-19?

In terms of the epidemic, I feel that Finland has a privileged position. If I reflect on my own experience, I have been through more difficult moments in my career. It is all relative.

I am doing fine; I spend a lot of time outdoors with my husband. In the winter, it was really refreshing when there was a lot of snow, and we got access to ski tracks right from our own yard. I am also practising pilates remotely.

If the internet connection is poor, I drive to Otaniemi to give the lecture. It helps maintain the rhythm, but at the same time it is strange to go to an abandoned building and then “meet” students there via Zoom.

In the autumn, I was able to give one face-to-face lecture, and it was really empowering. It is part of a teacher's identity. However, it was strange that when, during the lecture, I wanted to go and guide the students in their work, I could not go near them.

There is nothing new in remote work as such, it is the everyday life of a researcher. But now the difficulties are starting to become clear. In normal conditions, certain things progress effortlessly through interaction and even occasional encounters, just because I am present in Otaniemi. It is often enough to mention something about a matter in passing. But now, even the smallest matters require calling or writing an e-mail. It takes time and feels a bit foolish.

What are your expectations for the future?

Conferences are an important part of the lives of researchers, and remotely I have participated in conferences, where I would not otherwise have gone. For example, there are now many genuinely cross-disciplinary origami conferences. That said, interaction is also a challenge for conferences, as the most important aspects take place outside the presentations.

The cross-disciplinary Bridges Conference, for instance, was supposed to be held at Aalto University in 2020, and it has been postponed twice. We are now planning it for 2022.

I received a grant from the Magnus Ehrnrooth foundation to produce a book that combines mathematics and art. In other words, we will put down in writing the results emerged in the course over ten years.

In 2016, I was at the University of Monterrey in Mexico and held a course with a local architect. In Shanghai, we organised a Crystal Flowers mini-exhibition and workshops for schoolchildren, teachers, and university students just before the corona. We made a great number of contacts, but then suddenly, everything came to a halt. I wish that in the future, I will be able to increase international cooperation and find wonderful new contacts.

Further information:

 


Eveliina Peltola: Mathematics is beautiful because in it everything falls into place in a natural way

6. May 2021
Eveliina Peltola. Photo: Lassi Savola.
Photo: Lassi Savola

What are you researching and why?

I have started my assistant professorship of mathematics at Aalto, and I am also continuing in my post as professor in Bonn, Germany.

I research theories linked with mathematical physics. Physicists try to create models of the surrounding world and to confirm them through experimentation. Their mathematical foundations contain problems that mathematicians solve. The models also raise plenty of new questions that are interesting from the point of view of mathematics itself. I want to understand the surrounding world as a whole from a mathematical point of view and to ensure that the models describe what we want them to describe. This means that the theories have a strong foundation, and that the logical inferences are solid.

For example, my research includes a model describing small particles of magnetic materials with the help of statistical physics and quantum field theory. I am not yet involved in cooperation with Aalto's quantum physicists, but I hope that we might find topics of mutual interest in our research in the future.

I also study symmetries in the models, which are transformations that retain the relevant features of a system. Symmetry can be intuitive, such as rotation, or a more complicated mathematical structure. Preserving the characteristics can be literal, or it can mean statistical symmetry, in which the average features of a system are retained. In research I often start from things that are better understood through symmetry, and then I move to more difficult wholes, while building a theory. Symmetries are my friends!

 

How did you become a researcher?

It was partly coincidental. In upper secondary school I had no clear plan for my future and I was interested in everything.  I did not actually care much about mathematics, which seemed mechanical to me. However, being interested in sciences, I ended up at the Department of Mathematics at the University of Helsinki. My major was mathematics and I also studied physics and chemistry. I found that mathematics pleased me the most. I saw beauty in it - something greater than in the other subjects. On the other hand, my relationship with mathematics warmed up slowly, and I studied it for several years.

I feel that mathematics is beautiful because in it, everything gets arranged in a natural way. Ever since my days at university, the beauty of mathematics for me has been linked with symmetries: things started falling into place for me at a course in advanced algebra. Now I can see how this naturalness is also present in other areas of mathematics. My concept of the beauty of mathematics is abstract and intuitive.

Mathematics is a universal language that we need to get into before we can understand it. Although nowadays I make calculations that might look boring, the outcome can nevertheless be tidy, and there can even be sense in complexity. Mathematicians often get an internal intuition that guides things such as what kind of a result can be expected in a complex calculation. If the result is something different, I start to suspect that there may have been an error in the calculations, or in the reasoning.  I can also apply this intuition when checking the reasoning of the students.

Consequently, internal beauty and intuition concretely guide mathematical research, which is abstract in other respects.

Read more here.


The builders of digital trust

4. May 2021

More than 5.3 exabytes of information are transferred via the internet every day. This is an enormous amount: all of the words ever uttered in human history could fit into the same space.

The first internet message in history was transmitted over the ARPANET network in 1969. The message was meant to go from University of California UCLA to Stanford University, just over 600 kilometres away. But the phone booth-sized computer switched off before it completed the transmission.

The first-ever message was a stump – LO.

Programming student Charley Kline didn’t give up, however, and turned the machine back on. UCLA messaged LOG, Stanford replied IN – and the researchers even confirmed over the telephone that these letters had in fact been delivered.

Today, more than 300 billion e-mails and 60 billion WhatsApp messages are sent around the world each day. The number of internet users is approaching 5 billion and the average time spent online is some 7 hours a day, most of which happens on mobiles.

Our everyday life became digital in just half a century. What or who makes sure that our online lives are secure?

Concealed images and key pairs

One such person is Aalto University Assistant Professor Chris Brzuska. He specialises in cryptography or encryption methods.

The word krypto is of Greek origin and refers to the hidden or the secret. The Greeks of antiquity would tattoo secret information in image form on the shaved scalps of their slaves and send them out. Once the slave arrived at the destination months later, their head would be shaved again, making the message readable.

Modern cryptography is based on maths and computer science.

‘It researches and develops methods that protect systems and their users from adversarial interference. Whenever data is transferred over the internet, it needs to be encrypted to prevent outsiders from hearing or reading it,’ Brzuska says.

The work is done by employing mathematical algorithms and encryption keys that scramble the message into a format, which can be decoded only with the right key.

There are two principal approaches to encryption: the symmetric-key method and the asymmetric or public-key method. In the first approach, the same key is used to encrypt and decrypt messages, requiring both sender and recipient to either know the key or find a way to transfer it via a secure channel.

Often this cannot be done.

This is when the public-key method is used. It is based on a key pair of a public-key and a secret-key such that the secret-key is hard to compute, given only the public-key. The pair’s public key encrypts the message, while the private key decrypts it. The parties only need to convey their public keys to each other to enable encryption.

‘It’s a really cool concept, without which the entire net’s encryption would collapse in an instant. When Whitfield Diffie and Martin Hellman came up with the idea, few people could have thought that it would have a practical application. Back in the 70s, it was inconceivable that someone would want to secret information with complete strangers,’ Chris Brzuska says.

Read the whole article here:

https://www.aalto.fi/en/news/the-builders-of-digital-trust


28th Nordic Congress of Mathematicians

27. November 2019
28th Nordic Congress of Mathematicians, Aalto University, Finland, August 18-21, 2022

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