Transcript FACULTY OF MATHEMATICS AND GEOINFORMATION

FACULTY OF MATHEMATICS AND
GEOINFORMATION
Dean: D. Dorninger
TWO DEPARTMENTS
MATHEMATICS
SURVEYING AND GEOINFORMATION
FACULTY OF MATHEMATICS AND
GEOINFORMATION
DEPARTMENT OF MATHEMATICS
Institute of Analysis and Scientific Computing
Institute of Discrete Mathematics and Geometry
Institute of Mathematical Methods in Economy
Institute of Statistics and Probability Theory
INSTITUTE OF ANALYSIS AND SCIENTIFIC COMPUTING (E 101)
Magnetic field and potential of a
cobalt plate: multi-scale problem;
FEM-discretization for a non
convex minimization problem
Simulation of a solid under extreme temperature
and density conditions;
computation on fastest computer on earth: IBM
BlueGene/L
Bell-Award 2006 – world record!
INSTITUTE OF ANALYSIS AND SCIENTIFIC COMPUTING (E 101)
brain
stimulation
retina
stimulation
stimulationof
acoustic
nerve
electric
stimulation of
spinal cord
Analysis of the cardiovascular system:
modell identification (system of differential
equations) with coupling to medical databases
Electrical stimulation with nerval prosthesis:
modelling & simulation
with partial and ordinary differential equations
INSTITUTE OF DISCRETE MATHEMATICS AND GEOMETRY (E 104)
Algebra
Mathematical Analysis of Algorithms
Error Correcting
Codes
Convex und Discrete Geometry
Computational Logic
Fuzzy Logic in Medicine
INSTITUTE OF DISCRETE MATHEMATICS UND GEOMETRY (E 104)
Geometric Modelling and
Industrial Geometry
Differential Geometry and Geometric Structures
INSTITUTE OF MATHEMATICAL METHODS IN ECONOMICS (E 105)
Research Unit Financial and Actuarial Mathematics (FAM)
 Stock Price, Interest Rate and Credit Risk Modelling
 Derivatives Pricing
 Portfolio Optimization
 Ruin Probability, Financial Risk Management
 Life Tables (Chart: Logarithmic Male Mortality in Austria)
 CD-Laboratory for Portfolio Risk Management (www.prismalab.at)
(Joint Research with Bank Austria, Austrian Federal Financing Agency, FJA)
Research Unit Econometrics and System Theory (EOS)
Data driven Modelling
 Development of Methods (in particular for Time Series):
Modelling High-Dimensional Time Series, Factor Models,
Multivariate Volatility Models
 Applications in Economics and Business, Technology and Medicine:
Macroeconomics, Housing Sector, Forecasting of Business and Financial Data,
Analysis of Electroencephalograms
INSTITUTE OF MATHEMATICAL METHODS IN ECONOMICS (E 105)
Research Unit Economics (ECON)
 Simulation of Evolutionary Economic Systems
 The Role of Endogenous Preferences and Status in Dynamic Economic Models.
Reales BIP Wachstum (Quelle: OECD)
 Age Structured, Dynamic Models
 Macroeconomic Modelling
 Agent Based Computational Modelling
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Research Unit Operations Research and Control Systems (ORCOS)
 Development of New Methods for Model Based Decision Support:
Operations Research, Optimization, Control, Dynamic Games
 Applications in Economics, Management, Engineering, Social Sciences, Public Health Care
 Recent Topics: Heterogeneous Population/Economic Systems,
Control of Contagious Phenomena,
Indeterminacy in Multi-Stage and Stochastic Models,
Multi-Agent Modeling in Games and Auctions
INSTITUTE OF STATISTICS AND PROBABILITY THEORY (E 107)
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Engineering Statistics
Statistical Analysis of Fuzzy Information
Geostatistics
Probability Theory and Stochastic Processes
Reliability Analysis
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FACULTY OF MATHEMATICS AND GEOINFORMATION: STUDIES
Bachelor, Master, Doctorates and Secondary School Teachers Accreditation
Mathematics in Science and Technology
Mathematics in Computer Science
Statistics and Mathematics in Economics
Financial and Actuarial Mathematics
Mathematics, Descriptive Geometry
Surveying Science and Cadastral Research
Geodesy and Geophysics
Geoinformation and Cartography
Any student of the Vienna University of Technology has to take
courses in mathematics!
FACULTY OF MATHEMATICS AND
GEOINFORMATION
THE INSTITUTES OF THE DEPARTMENT
FOR SURVEYING AND GEOINFORMATION
Institute of Photogrammetry and Remote Sensing
Institute of Geoinformation and Cartography
Institute of Geodesy und Geophysics
INSTITUTE OF PHOTOGRAMMETRY AND REMOTE SENSING (E122)
Remote Sensing Example
Airborne Geo-data acquisition
Photogrammetry Example: Terrestrial Laser Scanning
Photogrammetric methods deliver …
Vienna University of Technology
and Karlsplatz in an aerial image
… 3D models (no images), providing documentation and
perspective views from arbitrary positions.
© ESA & EUMETSAT
Environmental Monitoring
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Changes in
 Snow and ice cover
 Soil moisture
 Vegetation, etc.
Due to climate change
floods and droughts occur
more frequently.
INSTITUTE OF GEOINFORMATION AND CARTOGRAPHY (E127)
Which questions arise when providing geoinformation?
geometry of streets
ownership structure
attributes of streets
Selection?
Strategy?
Solution?
Quality?
Presentation?
example:
car navigation
other data
from data
to information
Location Based Services
INSTITUTE OF GEODESY AND GEOPHYSICS (E 128)
Research Group Advanced Geodesy
EARTH: size and shape of the Earth, gravity field, Earth rotation, atmosphere, positioning (GPS, ...)
Research Group Engineering Geodesy
CIVIL WORKS AND NATURAL STRUCTURES
Shape, position, motion and deformation of objects
like bridges, tunnels, dams, high rising buidlings,
landslides
Setting out and monitoring
INSTITUTE OF GEODESY AND GEOPHYSICS (E 128)
Research Group Geophysics
Permafrost
Deep Alpine Valleys
Tiefe Täler
Lithospheric Structure and Dynamics
Microseismic Monitoring
Mikroseismik
Monitoring